I would approach this slightly differently – create a new MIDI track, set it to follow the Chord Track (Live Transform), and record your MIDI, and repeat for each additional voicing required. The MIDI input will be transformed to either the scale or chord events, and that way you can concentrate on phrasing and emphasis without worrying about “wrong” notes. You end up with harmony parts on separate MIDI tracks, but it may still need some editing to eliminate doubles etc.
If I understand correctly, the OP just wants to add MIDI harmony parts to an already-recorded MIDI melody line, with the harmony lines on separate MIDI tracks. In that case I would probably use a combination of the Chorder MIDI effect (possibly creating or modifying an existing preset) to generate the harmony and the Logical Editor to split the result onto separate tracks.
Another possibility would be to use MIDI sends, with the Chorder plugin as an insert. The main problem there is that it is not possible to select a MIDI track as the destination of the send, but it would work by looping a physical MIDI output back to the input, and recording that.
Finally, using the physical loop method above, you could play the existing MIDI track out and record it back in, but with the input track set to follow the Chord Track as above.
Yes I’d imagine it should be easier, and maybe I’m missing something here, but I suppose this is more in the realm of algorithmic composition, and there are other tools out there for that.