Well, to some extent, that's just the nature of neoprene. It's an insulator, of course, so if your feet are outside the water and it's not real cold, they're going to sweat. Maybe a lot. You could try some light neoprene socks, something such as the NRS Neoprene Wetsocks ($22). Most neoprene booties are 3mm, but these are 2mm, so they offer a bit less insulation. But maybe that's a good thing, in this case. They're designed to be worn under shoes, or in your case with sandals or something else that provides foot protection.
The "grip socks" you've heard of are Vibram Five Fingers (several models around $80). They're sort of a rubber/fabric glove for your feet. Each toe has its own, well, "finger." So you get the foot-feel of, well, your foot, and the protection of a light shoe. Vibram came out with these four or five years ago and at the time it seemed they had made these almost as a joke. There wasn't any clear market or marketing plan. But now the "no shoe" running crowd has picked up on them and REI can't keep them in stock.
Anyway, they're great for kayaking. They give you good foot protection and a little bit of warmth, but aren't as sweaty as neoprene socks. Try some!