First of all, forget harmonizing the entire text. I'm talking about reconstructing the Gospels' events into historical sequence. Succinctly, here's how that can be reasonably done.
If we posit two Nazareth homecomings and two fishermen callings, the sequence of major events in Mark and Luke suddenly finds complete harmony, even if minor details continue to diverge. Matthew's sequence differs only between chapters 5 and 13. After John the Baptist's beheading, Matthew's narrative sequence shows no contradictions with Mark and Luke. If we also posit two Temple cleansings, the sequence in John's Gospel also blends perfectly with the rest. (**There are other ways around this little problem, but for time's sake, at the moment, we begin by simply assuming those three points.** Update: see my response to Tim's question in the comments.**) So stipulated, we begin.
The first event to harmonize is Jesus feeding the 5,000. This dates JTB's beheading to the middle Passover of John's Gospel. The first Passover of John's Gospel comes just before JTB's arrest. Jesus left Judea when he heard about that arrest, and that the Pharisees were now more concerned about Jesus than about John. This brings us to a critical point of consideration.
Herod Antipas probably captured the Baptist somewhere in the Transjordan region, which Antipas controlled. Why, then, did Jesus leave JUDEA when he heard about this arrest? The only possible danger for Jesus was if he suspected the Sanhedrin might begin to consider arresting him for extradition to Galilee. At this point, it seems, the Pharisees just wanted Jesus to go back to 'Hicksville'. Wisely, he obliged their desire before they could hatch any plans.
For all of John's imprisonment, Jesus stays in Galilee (except briefly, in Jn.5). After Herod Antipas notices Jesus, the Lord withdraws from Galilee repeatedly, slipping into every neighboring country at some point except in the direction of Judea. After some period of these 'withdrawals' had passed, Jesus made plans to go back south. What had changed? The Pharisees would still want to extradite Jesus back to Antipas, and now the Tetrarch was actually looking for him! Why was it suddenly safe?
Sejanus must have died. Antipas must have had some kind of agreement with Sejanus for the Tetrarch to divorce his Arabian wife, effectively ending the treaty with King Aretas and jeopardizing peace in the region while Tiberius entered his 70's. Herod Antipas would not have risked everything for Herodias, unless he really did have a deal with Sejanus. So the caution Antipas [and Pilate also] displayed at Jesus' trial really must have been because of the climate in Rome. Heads of Sejanus' old allies were still rolling with the slightest provocation.
The point at the moment is that Antipas' caution did not begin at Jesus' trial in early 33. Antipas' caution began at Sejanus' death in late 31. Therefore, if the period of Jesus' withdrawals reflects a time after John's death when Judea was still unsafe to enter, then John must have died before Passover of 31. That makes the second 'half' of Jesus' ministry two years long. The missing Passover of 32 is most likely locatable around the time of the Temple Tax (Matthew's coin in-the-fish episode).
Incidentally, Jesus' visit to Tabernacles and Hanukkah could arguably go in 32 because that was after Sejanus had died, but 31 is not impossible, because Tiberius spread rumors all year long in 31 that Sejanus' life could be in danger. If Antipas got wind of what was coming, the Father - yes, we're getting spiritual now - could have told Jesus it was safe. That is a valid spiritual-historical consideration, especially if we take the word "sent" in its most immediate sense (Jn. 8:16, 18, 26, 29, 42; in contrast, Jn.10:36, "sent into the world", reads very differently.) The dubious level of safety could partly explain why the disciples do not join Jesus on this trip. However, it remains less than perfectly clear at the moment whether John 7-10 could belong in 31 or 32. The earlier date fits better with the overall structure of events and even with the development of Jesus' public discourse, but it requires Jesus to have special confidence that he would remain safe. However, this does fall several months into his period of withdrawals, and on the balance of all considerations the timing does seem to work. Cautiously, then, we should prefer 31 for these two months in Judea.
The last major question is whether John's imprisonment lasted the better part of one year, or two. The sabbath grain plucking incident occurs well in the middle of John's imprisonment in all three Synoptic Gospels. The fact that grain was ripe points to another missing Passover. Therefore, the first Passover mentioned in John's Gospel belongs in 29 AD, and the sabbath grain plucking must have occurred in 30. (Incidentally, the "harvest" Jesus mentioned in Samaria must have been the fall harvest. His reference to "white fields" was merely a mixed metaphor - not so uncommon for him, really!)
We now see a total of five Passovers - 29, 30, 31, 32 and 33 AD. Jesus' ministry in-between those Passovers was four years long. John was in prison for most of the first two years, and Sejanus died in the third autumn. This completely aligns most of the historical landscape for Gospel events. The rest falls into place very quickly.
One other incidental issue, first, is to consider that the death of the Empress Livia in 29 (most likely late winter in early 29) could have called Herod Antipas out of the country to pay his respects in Rome (and most likely also to firm up his relations, whatever they were, with Sejanus, because Livia's death was the start of the Prefect's big power play, and that fact was apparently obvious to everyone but Tiberius at the time). In any event, if Antipas did leave for Rome in 29 it would explain perfectly why Jesus gained fame all over Palestine without Herod noticing, and why the Pharisees went "to the Herodians" in Mark 3:6 instead of "to Herod". (That Antipas was in Rome has been suggested before, but considered implausible because there was no cause for the trip in 30 AD, in Hoehner's chronology.)
Our final task here is to work backwards from the first Passover. We need to account for at least 40 days after the Lord's baptism, plus some recovery time after such an ordeal, plus even more. There had to be some travel time - another trip to and from Transjordan and then to Cana and Capernaum - all before the Passover of 29 AD.
Regarding John's ministry, Luke tells us that "all the people were baptized" before Jesus came to be baptized. Of course we assume Luke means all the ones who-were-going-to-be-baptized, and obviously not every solitary soul in the land, but his phrase still suggests that everyone in Israel had a chance to hear about John that year, and to go to him. Because the 15th year of Tiberius can plausibly refer to all of 28 AD (by more than one method of reckoning, and we must admit we have no way to know which method Luke 'should' have preferred), it seems likely that John preached and baptized through all three festival seasons of that year.
Altogether, this means Jesus most likely came to be baptized around the turn of October in 28 AD. His wilderness trial filled out the rest of 28, leaving three months for recovery, recruiting, moving his family to Capernaum, and final personal preparation before his first public Passover, at which he essentially declared himself the Messiah by cleansing the Temple.
That concludes the entire skeleton of what I contend must be the one, most likely, most plausible reconstruction of the Gospels' events, in chronological order and with full historical context.
28 AD - In the fifteenth year of Tiberius' rule, John the Baptist begins his ministry in the wilderness. John baptizes all spring and summer, preparing the way for Jesus. In Autumn, Jesus comes to be baptized. He is 33 years old. (Luke says "about" 30.) Jesus spends the first half of winter alone, fasting and being temped in the wilderness.
29 AD - Jesus recovers from his testing at home in Nazareth. John begins baptizing again in early Spring. Jesus’ disciples begin to follow him. Passover: Jesus visits Jerusalem and clears the temple. Herod Antipas divorces his Nabatean wife (the daughter of King Aretes). John the Baptist is imprisoned by Herod for criticizing the divorce. Herod (possibly) sails for Rome after hearing of Livia's death. Jesus and his disciples flee Judea after John's arrest. Briefly, they visit Samaria on their way back to Galilee. Peter and Jesus' disciples go back to normal life after their trip, as anyone would. Jesus calls the fishermen the first time and invites Peter to go to other towns, but Peter stays in Bethsaida. Jesus travels alone the rest of the year, and rests for some time during winter.
30 AD - Spring: Jesus calls the fishermen the second time and they begin follow him. Jesus calls Matthew. The disciples pick grain on a sabbath. Jesus officially selects his twelve apostles, some weeks before Passover. They travel all over Galilee together, living on fishing profits and free heads of grain. Jesus' fame spreads far and wide. Soon, a few wealthy women begin to travel with the group, providing for their needs financially. Jesus stays in Galilee all year - he does not go down to Judea. Before autumn, Jesus takes his disciples along on his second Nazareth homecoming. As the fall harvest approaches, Jesus sends his disciples out in pairs to many cities. Herod Antipas (possibly) sails back from Rome by October. Again, Jesus appears to be less active during the winter. He is probably resting.
31 AD - Herod Antipas has John the Baptist beheaded sometime before Passover. Shortly after, Herod realizes the reports he's been catching up on are about Jesus, not old news about John. Herd begins trying to see Jesus. Jesus' disciples, having traveled through the winter, find Jesus in some town (Tiberias or Capernaum?) just before Passover. Jesus feeds the 5,000. The people in Judea hail John as a martyr, and condemn Herod for his death. In Autumn, Jesus finally visits Jerusalem again, and stays through December. In October, Sejanus is finally killed, in Rome. This news is confirmed in all Palestine some weeks later. Antipas and Pilate begin ruling with additional caution. Jesus remains safe in Judea for two months, from mid-October to mid-December. He does not seem to rest much this particular winter.
32 AD - Jesus travels up towards Syria, near Tyre and Sidon. On their journey, Jesus begins preparing his disciples for his death. Peter confesses that Jesus is the Messiah. Jesus is transfigured on a mountain with Moses and Elijah. Around Passover time, Peter obligates Jesus to paying the Temple-Tax. After Passover, Jesus leaves Galilee and begins a year-long tour around Judea. They visit at least 35 cities all over Judea. Jesus repeats teachings in Judea which he'd been giving in Galilee since two and three years ago. Jesus and his disciples find a second home in Bethany, with their friends Lazarus, Martha and Mary. Three things prevent the Jews from laying hands on Jesus all year long: He keeps avoiding Jerusalem, the people are still upset about John's martyrdom, and Herod Antipas refuses to allow extradition. Because of the current political climate, Antipas cannot risk causing more unrest in his kingdom/tetrarchy.
33 AD - Jesus has become so popular the Jews have no choice but to plot against him. At what is only the second Jerusalem Passover of his five Passovers in public activity, Jesus cleanses the Temple again. The Pharisees and Herodians try to trap him with a coin, but the Sadducees finally have to strong arm Pontius Pilate into using Rome's garrison to arrest Jesus. Jesus is tried, crucified, buried and ascends. Then he appears to the disciples and gives them the Holy Spirit... and THAT is only the beginning of the next chapter in Jesus' Story!