Summer is hot here, RT between 82-86f
I'm sure it can be done, but personally I wouldn't want to keep pizza dough for a long time at 86F.. My personal experience is that the hotter the dough gets, the harder it gets to make pizza.

Maybe try to keep dough temp down a bit, like use ice water to mix it, keep it in a cooler or wooden box to slow down it's warming up process, etc.
I also saw that you said that your flour doesn't like to drink a lot of water. This to me is a sign that it's weak flour. AFAIK a weak flour doesn't need a long maturation period. If you'd want to do all at AT, you could experiment with 2 hours in bulk, and then 4-7 hours in balls.
Or if you go for the fridge method, take care about the dough temperature. The warmer the dough gets when you make it, the faster it will ferment (problem is bigger with a big dough, as it takes longer to lose heat). Most of us don't have fridges that stops fermentation completely and immediately.. Maybe in this scenario try a short time (or none) in bulk at TA (or even put it in the fridge between S/F if you do them), then fridge and finally 4-5 hours in balls.