Sorry for undigging the old topic, but this dough sticking was really a big issue for me!
First up, one issue is speed. Have everything ready, put it on the pizza and onto the stone. The faster the better.
But sometimes things take a bit longer, then looking into other helpful things....
Sometimes it's a practice thing, other times the dough might be too sticky or not enough flour. You can try rice flour, semolina, etc. instead of regular flour.
Flour/Semolina did not work for me. It goes wet fast and sticks. However, rice flour does not sucks much water and stays dry. Hence your pizza does not get stuck on the peel - even without lightspeed work! And rice flour has one more added bonus: it can handle heat! Flour/Semolina goes black on the stone in no time and starts to smoke - rice flour goes just a little bit darker.
Took me really a long time to find out about that.