Your efforts thus far are sound but the merits of what you might attempt to do are questionable. Everyone has those ground-level suckers which actually do develop roots but the benifits to the mother plant are more doubtful- like planting 2 plants together.

If you remove those suckers and insert them in growing media - (I did 48 this morning in 5 minutes before going to a farmers' market) then in a few weeks you can replant them as rooted plants at a reasonable spacing; I use 23" in-row spacing this year for single stem plants in high tunnels. Square foot yields are hard to beat using that method.