"Should I do everything I can in BIAB, and then transfer the files to Reaper for final tracking and editing,
Yes, Yes a 100x Yes.

Or, "... well that's the way I do it".
One thing you should quickly learn about Reaper, which has not been mentioned and was not one of your criteria, but Reaper is "rock solid". Meaning it does not freeze of fail. Once you start working in Reaper you will learn how wonderful that is.
good luck.