I get this. Most styles are a bit "heavy" handed. Sounds like a band that had too much coffee.

In MIDI it is easy.
For myself, I began by editing all styles I used, lowering the velocity of the bass and drums, changing the bass instrument to Upright Bass and all drums to Brush drums (all of that inside the style) and disabling piano and guitar and strings and all the rest... Later on, I began making my own styles, not being satisfied with what was already on offer, even after tweaking.

Styles with other percussive instruments are sparse, but there is an Oregon style that will cater to these needs. Would indeed be a great idea to have styles with modern percussion.

BTW, your question about chord inversions and open strings and all. The style maker doesn't allow you to specify all of this. That would be a very complicated algorithm altogether. And I am pretty sure Realtracks won't allow those options either.

Maybe this could work for you: lower the velocity of the accompaniment tracks like piano, guitar. Making it more discreet will open up room for your playing and singing, sax or trumpet. If you find other solutions, let me know, would be great.

Biab, Kontakt, Sampletank and lots of nice libraries, from Fluffy audio to Abbey Road drums.
Check out these great contemporary Jazz Styles: www.jazzstylezz.com