@jazzmammal
As far as getting away from the 'So What' harmonic rhythm issue is concerned the only way to go is to be 'tune specific' using holds, shots and rests. Or else a midi input single note accompaniment counter melody that suggests the tune then using the melody harmony feature to create chord voicings out of that.
The good thing about BIAB is you can approximate a lot of polychords using respellings; inversions of altered dominants over an alternate bass. e.g.Bmaj/Cmaj = F#13susb5b9/C.
If you want to go further than that then just bounce the generated chords to the melody channel and use a one-note melody harmony to add a note to each chord in the sequence. (you need a new chord sheet for that one note though).
A lot of this creates extra work so if you do have a midi file of the tune or even a score you can convert to midi I'd much rather roll my own style that way if possible. But then how much modern repertoire in midi can you find on the net?

Alan

PS Here's an example of an 11/8 modal accompaniment in midi with 'unsupported' chords using holds and rests to get an acceptable result. The tune in question is the Ralph Towner/Oregon classic 'Distant Hills' but using a non-'Oregon' style to get the ECM records version. You'll have to supply the melody though!
If you want I can post the very specific scales Ralph Towner uses for the chords.

Distant Hills