I would somewhat challenge that simple understanding though, on the basis that down the page in 1 Corinthians 15:35-54 Paul dismisses as foolish the idea that anyone would be resurrected in their own body. It's not even a fringe view.
Ehrman for example says the exact same too: "
Here Paul stresses that Jesus rose from the dead in a "spiritual body."" That's a direct quote of Paul's words, btw: "spiritual body."
So Paul isn't actually saying that Peter, James and the 500 actually "saw" a zombie Jesus in his old body. Somehow they "saw" Jesus just like Paul did, as a risen ghost.
In fact, Paul's seeing Jesus is described in 2 Corinthians 12, from the top of the page. He describes "a man", which is hinted and understood as being Paul, being taken to paradise, where he talks to Jesus. I.e., he doesn't even see the "spiritual body" Jesus on Earth, but in a whole other realm.
It is a fair guess that the other 500+ people "saw" Jesus in that realm too.
Actually an even better translation is not as much that they "saw" it, but that he "appeared" or was "revealed" to them, or was somehow "discerned" by them. The subject of that sentence is Jesus, not those guys. The verb "horao" is also used quite EXTENSIVELY as basically "seeing with the mind", so to speak, rather than with the eyes.
This is actually rather crucial to the MJ theory. Paul doesn't actually say anyone actually ever saw Jesus's earthly body, before or after. He only says that Jesus was somehow revealed to them after his resurrection, which, as we established, was as a spirit. Indeed Paul spends half a page debunking as absurd the idea that Jesus could have risen in his old material body, so, you know, that's not what those guys could have seen. As such, it's not really crucial that those guys ever saw Jesus in a material body. That's not how they recognized him.
Edit: In fact, other than some mass hallucination (e.g., caused by Ergot), it's rather unlikely that ghostly Jesus would be revealed to 500 different people at the same time as an actual vision. Their somehow just "discerning" that, yeah, the scripture says he already rose is a rather more plausible version.
So here's a possible timeline: Peter somehow "discerns" that the messiah already rose. Possibly in a vision, possibly in a dream, or just has a flash of enlightenment while poring over the scriptures. He TELLS the 12, who also "discern" that, yeah, you know, Peter is right. Their messiah already came and already was resurrected. Then 500 followers of this cult agree to it. James arrives a bit later and is convinced too. Meanwhile way later, Paul has the same revelation in a vision, and proceeds to preach it all over the place. And when he finally meets Peter and James, of course they don't have anything to add to his version, because both reconstructed the same thing from the same scriptures. In fact, Paul's version may even be more detailed than theirs.