Actually, I would NOT opt for the highest expansion, because that stuff will put a lot more pressure on the back of your cabinets and bow them in. I think you'd probably want the low-expansion stuff that's intended for doors and windows, which don't take warpage well.
I'm also having trouble understanding why you'd have cold air coming out of your bottom cabinets but not from the wall above the cabinets. Is there no stud wall behind those cabinets? Is there no pre-existing insulation?
FWIW, I recently did the "drill holes and inject foam" thing with the uninsulated lid of a cooler (who makes a cooler and fails to insulate the lid!? a mfr for Walmart, of course!), and it worked great. Drill holes, inject foam starting at one end, let it sit overnight, and break off the over-expanded bits the next morning.