You don’t need an external DAW on the BK9. Set the Recorder to record MIDI, not audio, play and record the accompaniment. Save as an SMF. Open it in the 16 track Sequencer, then edit, add extra Parts, whatever. Save as an SMF, then do fine tuning in the Makeup Tools.

You can get a bit tighter accompaniment by initially recording the first full style capture with the tempo slowed down enough for you (and the arranger engine!) to not struggle being precise with your timing. Then bring back to full speed for the overdubs.

This can also simplify getting the chords and inversions correct. Just play the chords in your RH, and the correct bass inversion note with your LH (like you would playing a simple full piano part) and do not activate any keyboard sounds at all. The arranger will still recognize the chords if set to Full Keyboard.

You certainly get easier editing using a DAW, but you can still do full recording using the BK9, even to the point of recording the audio after all is finished…