How about recording into RealBand? It comes with BIAB and directly loads the BIAB song files.

I'm not a "pro" at this, but I have had pretty good success with creating my song in BIAB and then load the SGU file into RB and recording bass and guitar tracks and other instruments there. I'll make edits and do the track processing there as well. For my uses there is no real need to export to another DAW since so far RB does everything I need for what I'm doing. One of the benefits for me is that I can visually watch the progression of the BIAB song chord changes pretty much the same as in BIAB, etc. while recording in RB. After I found that I can use most Reaper plugins in RB, that pretty much sealed it for me. It works for me, but like I say, I'm not a "pro".