What about using shade cloth? Curtis Stone (also known as the urban farmer - he's on youtube and also has a book out) has a
video about growing lettuce in a hot and humid area by using shade cloth and also cooling the lettuce by watering a couple of times/day. Also, the variety of lettuce matters.
A bit of work for one's own lettuce enjoyment, but if the enjoyment is great
enough, it may be worth it. :-)
Here is the video I am talking about.
https://www.youtube.com/watch?v=PWbArzUCZu0