Summary (so far) of proven repeatable (by many) import into BIAB issues:
- Wong Key <== root issue BIAB is importing in XML 3.0. All other apps are using 4.0.
- Wrong Time signature <== root issue BIAB is importing in XML 3.0. All other apps are using 4.0.

Still investigating
- What does it do with note-based lyrics
- Why are Maj7 chord spelling missing in some examples
- Rhythm slashes showing as notes

Notes:
Trevor's export from BIAB then import into BIAB test:
- BIAB is using Music XML 3.0 the rest of the world is using Music XML 4.0 <== root issue
- FYI, I did Trevor's test of output then input in BIAB and all but lasts chord was wrong compared to input when using an offset of 0. I also brought it into Musecore and exported it as mxl 4.0 and strangely enough it was close to accurate when importing into BIAB. The only variation was an extra part break at the end of the song.

I recommend people read the Music XML 4.0 spec to understand its purpose:
https://www.w3.org/2021/06/musicxml40/

MusicXML 4.0 was released in June 2021 and all current scoring apps use it, so BIAB is 3 years behind.
I think we know enough now to consider this a feature request to update BIAB to the standard for Music xml for the last three years.

Studio One (latest version), Win 11 23H2 , i9 -10940X 3.3 GHz, 32GB Mem, a 4K 40" monitor, PreSonus Studio Live III Console as interface/controller. secondarily test on Reaper, Cakewalk, and S1 on Surface Pro 3 Win 10 (latest versions).