I think my inclination would be indeed something along the line of sneakers --- quick drying (non-goretex) trail runners or something along that line. I'm thinking of a pair of old jungle boots I have in a closet somewhere from my Army days, with little plug vents just above the soles. Only much, much better in terms of being able to vent and dry out.

If cold enough, I'd add neoprene socks --- sealskinz or seirus storm socks or the like, but in the summer for you, just thin liner socks.
If you feel the need for gaitors, then something there too that is light and won't hold a lot of water for a long time, but I'd be inclined I think to just go without.

As long as I can dry my feet and have dry socks to sleep in at night, I've not found it to be a problem having wet feet during the day, and in the conditions you describe I think it would be worse than pointless to strive to "keep your feet dry" with any sort of waterproof footwear.