Well, actually there's that. Paul's conversion, as well as the dating of his epistles, are one of those cases where the dates are just pushed as low as possible to seem more authoritative, and the intervals given are narrower than any historian would give on any other domain. A lot of it is also based on the novel that is Acts and on completely unsupported pious fictions, like his beheading by Nero.
So while that is a solution, it involves saying out loud that basically the whole dating of it is BS. I'm not convinced that most apologists would find that more palatable
That said, Paul himself does give us some margins for that. He says he fled Damascus under king Aretas. Well, that can't possibly have happened before 37 CE, which is the lowest supportable date for the town being given to king Aretas, nor after 40 CE, when king Aretas dies.
In fact for the beginning it couldn't have been earlier than March 37, when Caligula took the throne, since he got it in a peace settlement with Caligula. Though more realistically it wouldn't be on the very first day Caligula took the throne, or anything. It's also unlikely that it would be exactly before king Aretas died, since we see in other places that Paul is overly eager to take credit for the death of an opponent and claims HE sent that opponent to hell. I'd think if Aretas died right as Paul was running from Damascus, Paul would have beaten his own drum for that miracle.
Since Paul gives us the information that he first went and preached in Arabia for an unspecified amount of time, then returned to Damascus where he stayed 3 years. So even if his stint in Arabia was just a couple of days, that would give us an absolute upper date of 37 AD for his conversion. Though a more realistic date is something like 35-36 AD.
Let's take around the end of 36 AD for a conversion date (he preached just a few months in Arabia, but still, enough to be worth talking about that), so basically more or less right after the crucifixion.
The problem there though is that both Paul and Acts say that Paul actually spent some time persecuting Christians and was pretty infamous in 3 provinces. Not only he needs time to build up that reputation, but also Christianity needs to spread in those 3 provinces first.
We are told Jesus was nailed on Passover, which in 36 CE would be on the 29'th of March (by our Gregorian calender.) Add 40 days or so after the crucifixion, and the Christians don't even go public with their faith until mid-May. And if Acts is to be believed, it's not like they instantly send missionaries all over the place. In fact, at first they seem to just dick around in Jerusalem.
So anyway, for 36, we have basically half a year for Christianity to spread AND for Paul to build quite a reputation, in spite of the fact that he couldn't really operate overtly and had no jurisdiction anywhere. The same Pilate, who, we're told was pretty quick to kill at the slightest sign of sedition, wouldn't hesitate to behead Paul right there and then if Paul started taking the law in his own hands and executing people.
Things are starting to look a bit compressed there, you know?
Plus, it would be weird for Paul to call himself "one untimely born" (read: converted) if he basically had seen the risen Jesus around the same time the apostles did.
Well, at any rate, there are other things that Paul mentions and which serve to anchor the dates.
E.g., after his first trip to Jerusalem, he takes 14 years until his second one. (Galatians 2:1) Incidentally, that also tells us that Paul is still hallucinating Jesus, it wasn't a one-off affair. He says point blank that he went there in response to a revelation. (Galatians 2:2.) So, yeah, he might not be the most stable or reliable of sources.
It may not be apparent, but that 14 years is going to be a problem in a jiffy.
Because if he returned in 40 CE, then 40+14=54 CE for his second visit to Jerusalem. So, you know, his missionary journeys wouldn't even start until 54 CE.
BUT by the end of his ministry fate sees him tried by Gallio. Well, an inscription in Delphi mentions Gallio as proconsul, and the year given is the 26'th acclamation of Claudius. This time it's an official inscription from exactly that time, so we can have some confidence that it's not a year pulled out of the ass. Claudius received his 26'th and 27'th acclamations in the year 52 CE. (Originally they were only after victories or such, but by then the Senate was giving them willy-nilly to emperors, usually more than once a year.) In fact the 27'th is mentioned on an inscription from an aqueduct he dedicated on 1 August 52, so he must have gotten the 27'th a bit before that, and the 26'th, obviously, even earlier. We're talking the first half of 52 CE in any case, not December.
Proconsuls served for 1 year, very rarely for 2 years.
So Paul could only be tried by Gallio in 52 AD, let's say plus or minus 1 year, in case Gallio served two terms.
Paul is brought to Gallio about a year and a half after he arrived in Corinth, so if he went straight to Corinth from Jerusalem -- and everything in between didn't actually happen -- if he came to Jerusalem in 54 CE, he couldn't be possibly tried by Gallio earlier than 55-56 CE.
So we have a time-warp again. If Paul came back in 40 AD, he can't be tried by Gallio earlier than 55-56 CE, yet Gallio couldn't possibly try him outside of 51-53 CE.
Etc.
So basically, even if you squeeze events to solve the crucifixion-conversion time-warp, now you just created another time-warp.
The only solution for this time warp is to push Paul's conversion back and have him return from Damascus in 37 CE or thereabouts. But now we have the first time warp.