I've had MANY nights that go like this making pizza. My last cook, I couldn't get the fuel to really burn, so we had smoked pizzas. Sounds awesome when I read it, but trust me. It wasn't. I lost many to the back of the grill, mostly before I got a wooden peel to use for loading the pies. That was a game changer. Oh, and using an obscene amount of corn meal. I'm with you though. I'll wait until it warms up to try to use my KP.
I can't endorse Ken Forkish's book enough for pizza dough. It's only about $20. The recipes are simple. He teaches you about the importance of time and temperature as ingredients in dough. Even the horrible pizzas I made last time, the dough was great. I've made all the other recipes out there which are all good, but what I made with his recipe was exceptional.