And the feet thing is part of why I tend to avoid shoes in summer, since it means my feet are slippery in my sandals.

Yeah, sweating feet slipping around inside a sandal is kind of gross. I wear Chacos when I have to have shoes on; they have a pretty good grippy surface on the top of the sole which helps. And even when I "have to" wear shoes, I pop my feet out of them almost immediately upon sitting down anyway, which helps. I'd give you my standard answer advising eschewing shoes and socks in order to keep feet dry, but I suspect you're probably barefoot most of the time anyway.