For the C4maj (C,F,B) I use F5b/C. It gives you an extra note you don't want though as does using the G7/C option as a workaround.
I take your point about assigning scales to the chords. Once you start using inversions like B7susb5 for the Locrian chord you wind up with embellishments that don't belong because BIAB treats every dominant as if its a V chord.

Regards

Alan