Yes, there is some "play" in the numbers, of a year or so
But, the Crucifixion was
circa 30 AD +/- 1. If 30 AD, then Paul converted in 31 AD; and then was martyred in 66 AD. Paul's last letter as a free man = Titus, written from Nicopolis in western Greece, where he was wintering. And, in the winter of 66 AD, emperor Nero arrived near to Nicopolis,
en route to Greek Olympic-style games. If Nero had "dropped in on" Paul, practically; then Nero would have claimed that Paul was an arsonist, complicit or accomplice to the fire of Rome; and that Paul had betrayed Nero's clemency granted in 62 AD, to burn Rome in 64 AD. Nero would have summarily dismissed Paul to execution in Rome.
The
martyrdoms of Peter & Paul are traditionally associated with June 29. So, dating Paul's martyrdom to summer 67 AD, a few months after being arrested in winter 66 AD (and during which few months Paul would have written 2 Timothy), seems plausible. So, maybe Paul was martyred in 67 AD... converted in 32 AD... Crucifixion in 31 AD...
somehow Sejanus is involved; Philo wrote about Sejanus, implying that Jews feared whilst he was in power, which fear could account for the desire of Ananias & Caiaphas to placate Rome. Sejanus fell from power in late 31 AD, so being the latest date for the Crucifixion, after which Tiberias had removed & executed Sejanus, and issued a decree for toleration of Jews.