I have a Lodge 15" cast iron pizza pan which I tried using on my grill this afternoon. After 30+ minutes the pan was beautifully hot, about
650 degrees (F). Unfortunately, at this temperature the seasoning had vaporized. Oops.

I planned to follow a technique similar to that described in the thread "Pizza method page (cast iron pan + broiler)" (I would link, but new members are not allowed to, I guess). I would
cook the bottom first, then immediately top and finish the pizza under the broiler. Using this technique on the stove top and in the oven, I've had moderate success, however I've been looking for ways to reduce the total cook time further (to reduce the dryness which can occur with more than 5 minutes of cooking). The grill seemed like the perfect solution.
I laid down my dough and in about 90 seconds it had puffed up beautifully,
but the bottom was beyond burnt. This confuses me, because the floor of brick ovens are much hotter than my cast iron pan, yet pizzas cooked in them turn out just fine, and with longer cook times. Does anyone have suggestions as to what might have happened, or how my next attempt should be different?
Without seasoning on the pan, it did seem to stick quick a bit more, and those parts really burnt up. This could be the central problem? But I don't know how I can lubricate such a hot pan. Oil and extra flours won't work. In brick ovens, no lubrication seems to be used (other than ash, I suppose?).
By the way, my dough is 65% hydration, using high-gluten bread flour (14.2%), and cold-fermented in the fridge for a few days. I flour my dough liberally with AP flour while it's still a ball, then knock off all excess flour, stretch it out without additional flout, and transfer to the peel and then to the pan. Doesn't seem like much excess flour hangs onto the dough this way, but I could be wrong.