Yeah, summer here kind of sucks. Judging by the wind recently it is already here too, I wouldn't expect many more good days at this point.
There are some decent thermal winds in the summer, however. If you have a big kite, you might be able to kite a few days per week. Not really with any power, or able to go upwind, but you'll be able to ride a bit and practice, at least.
It seems to get worse the farther south you go. Jupiter gets some nice sea breezes over summer, but every time I've checked Islamorada it's always been dead. I would guess that there isn't enough land to create the temperature gradient that drives the wind up in the summer.
Yes, learning in the waves kind of sucks. The good news, is that we don't get waves during the summer either. So you might be able to catch some of the thermal wind and get up and riding before the waves really kick in. If you drive about 30-45 minutes south, the waves will be dramatically smaller as well - Jupiter is about as far south as you can go to get surfable waves, farther south than that and it turns to mush. I've heard it's because the Bahamas block most of the swell.
If you *DO* find a day where there is a great forecast, Anne's Beach is probably the best spot to learn, it's super flat water and shallow. The launching area is pretty sketchy, so definitely get your kite control down before heading there.
Matheson and Crandon both have a ton of rules and restrictions (and cost money), so I've never bothered going there. Miami is kind of a clusterfuck for kiting so I try to stay away.
If you're willing to take a trip, the Outer Banks in North Carolina are firing during the summer and it's ideal conditions for learning while it's dead here. Steady wind and knee to waist deep water in the Sound.
Either way, you'll get some kiting in, it just kind of sucks. It's the perfect time to get used to getting up and riding consistently though, I'm sure if you catch the windy days over the summer you'll be ready for next season.
Pray for hurricanes!