The sync problems have nothing to do with 24 vs 23.97.
The video capture is frame-by-frame, so the video is rock solid whatever speed you want, depending on the pulldown you choose.
The audio, however, is captured using a mechanical 16mm projector, a completely different machine than does the video capture. It has a motor and belts and gears etc., and naturally will vary slightly in speed due to different tensions on the belts as the film mass moves from the supply reel to the take up reel.
It is a trivial matter to sync something at the beginning, then move to the end and stretch the audio until the end also aligns. But, given the sway in speed over the course of the audio capture, parts in the middle will still be way out of sync.
My workflow was that I synched the beginning and the end in a Vegas timeline. Then I'd go back to the start and watch. When it drifted out of sync, I would insert a cut in the audio timeline, and stretch/shrink both sides until it was aligned again. I then would have to go back and make sure the earlier part was still in sync. Then I'd continue to play forward until the next time it went out of sync. I'd guess that by the end of a reel there would have been about 20 or 30 cuts.
It is complicated by the fact that the original film wasn't always perfectly in sync either. There are some spots where overdubbed voices and foley sounds don't match perfectly.
I don't know how well the PSB audio would synch with the GOUT, because I don't know how well the 16mm video matches the GOUT video. If they are identical, it would be easy to simply stretch it to fit. I suspect there are going to be enough micro-differences at scene changes to make synching with GOUT tedious, but easier than what I had to do.