I often want to do the same, and I'm always looking for a better way. Never tried your way, perhaps tomorrow.
What I do (and this puts each hand in a different track, not clip lane as you want) is select LH notes in PRV (in say track 4), cut, then
paste special to track 5. Pretty quick. Be sure the
now time is the same as the note on time of the first cut note. And for good feedback have tracks 4 and 5 selected in PRV.