Star, you'll have to adopt my technique. I play full chords in the left hand, mostly four notes, and generally keep them in the octave above middle C. I play root and rootless chords so I don't have to move my left hand too much. That way I can nail the chord on (or off) the beat. Doesn't matter what the right hand is doing unless I'm not playing a chord in the left hand. Then I play the chord in the right hand. That's where the full fingering comes in. Works quite well on the piano too without any accompaniment.
Bryan