I just use the "Write BWF (bext) chunk" to write the chords into the wav file.
To get the the chords from RB into REAPER I have to save to BB SGU then export the Midi Chord Output track from Biab into RapidComposer then save the midi again to get the Chord Markers then drag into REAPER.

I have been requesting features and fixes in RB for years and years, it is very, very, frustrating, so don't expect too much.
There are many great suggestions here but they never really get picked up.
I think at the end of the day BB Win/BB Mac need a Cross-platform 64bit re-write and have a Win/Mac VST version instead of RealBand.

I do Beta testing for RapidComposer and just about every feature requested is implemented in a very short time.

BB and RB are fantastic for what they do, nothing else does it, but just need modernizing.