Here's one aspect of the issue, just for starters - why did Herod Antipas say "up to half my kingdom"? Does that only prove he was drunk? Does that simply mean he assumed she wouldn't ask for so much? Or is the truth more complicated? Giving away territory, if the offer was serious, could hold a different significance politically if it happened in early 32 AD. It seems impossible to tease out any solid implications, but we ought to ask these questions anyway.
Is there anything about Antipas' statement that makes it seem Sejanus was alive or dead? "Take half my kingdom" could be the brash statement of a confident ruler secure that Rome would never approve it. Or - if Sejanus was dead - it could be the tortured brinksmanship of a man in the throes of depression at the very peak of anti-Sejanus reactionism, slipping out because of the alcohol? Or - again - was it just a safe bet she wouldn't bite?
Clearly, we don't know, but we can't even venture to guess because we don't know how drunk Antipas actually was! Does it require sobriety to feel political peer pressure in the matter of keeping an oath? (The request, regret and decision came "immediately" and "in a hurry" according to Mark; Herod's following-through is another issue entirely. But at the moment, we're just talking about the promise.) Or was Herod an accomplished drinker who felt few effects? Without knowing his blod-tox levels or their practical effects, we have zero ground to interpret any political context from Herod's promise that night.
Chronological work in other areas can tell us whether Sejanus was alive or dead when Salome did her dance, but we won't get very far from the political phrasing of Herod's promise, "Up to half my kingdom."
Stay tuned for blog posts on other aspects of this question and it's implications for New Testament Chronology.