I still don't understand how the keyboard is supposed to distinguish between solo notes or chord notes in full mode. I thought that as long as three notes were pressed the chord would be recognized, and you could tinkle over top till three more were addressed. I see no disadvantage in assigning the L & R sounds to the SAME tone, and playing in split mode, so ONLY the chords you send will be the triggers. I can't imagine wanting a moving solo line to be the determining factor for my chord changes.
Split mode allows for more sophisticated chord changes to be used without affecting the voicings in the right hand....and vice versa. Sometimes, a simple triad is all that's needed in the arranger, as long as the right hand is doing something juicy and creative.
I don't actually use the single finger mode - I use a mode that allows MAJ chords with one key, MIN with 2, but any other chord may be fingered also. This allows my left hand to maintain the "feel" I use when playing bass lines. I just don't like using big chords if I don't have to. It ties up too much thought process for me.
I can't imagine the split mode NOT being the mode of choice for acurate two handed piano technique. Just asign both sides of the split to the same sound.