Jonathan,
I have seen this problem with many round trip projects involving audio with my DCP work that involved FCP in the roundtrip.
I don’t have 100% confirmation but the error seems to related to the fact the FCP, when export is involved, does NOT use 23.976 for 24p frame rates but has math errors, probably rounding e.g. 23.98 or other rounding errors related to XML and other imports/exports. The only way I’ve been able to deal with this is to use OMF out of FCP and use that as the audio base which appears to not have the error. Unfortunately for many work flows, that does not work.
So I suggest export the video on it’s on, without audio from FCP (not clear if this is what you are doing) and the audio as OMF. In my experience, that does let 24p projects sync on round-trip.