Home-grilled pizza

This is not a pizza review, but one of the nice things about having a blog is that it is, ultimately, a self-indulgent exercise, so you get to prattle on about yourself now and then.
I didn't hit any pizzerias over the weekend, as I got the itch to make my own pizza, which I do every couple months or so. I made four pizzas, all different, probably about 10" across on average, which I baked on a pizza stone that I had set in my barrel-style charcoal grill.
Now I know that "grilled pizza" generally refers to a pizza cooked right on the grill grates. That involves putting a "naked" disk of dough on the grates for a minute or two, then flipping it over and adding toppings to the just-cooked side and cooking it a bit longer.
That's not what I wanted. My thinking instead was that I could achieve far higher temperatures in my grill than in my home oven, which tops out at 550. I wanted to get closer to the temperatures that are reached in commercial pizza ovens, or even professional wood- or coal-fired ovens, which are typically in the 800-degree range, resulting in a crust that's crisp on the outside, and slightly charred, but not burnt or dried out (at least if the chef, or pizzaiolo, is paying attention). I put the stone in right after lighting the coals, so it could heat up gradually, to the side of the coal bed. Once I was sure that the coals "took," I shut the lid but opened the side vent all the way to get a good air flow.
The results were good, but next time I need to make some adjustments. I didn't want to start baking the pizzas until the coals had turned gray, but it wasn't long after that point that the temperature inside the grill started to drop. When the first pizza (a white pizza) went in, the built-in thermometer was maxed out; the temperature must have been at least 700, and that's a conservative estimate. It came out great, just what I wanted, but by the time the second one went in, the temperature was already dropping; the coals had passed their peak.
A related problem involves getting at the pizza. With a professional oven, the pizzaiolo can check on the pizza, rotate it, etc. throughout the cooking process, without much loss in oven temperature. In fact, coal and wood ovens don't even have doors, just openings in the front.
I had to open the grill lid each time I wanted to check on the pizza, though, which let precious heat escape. I tried to minimize the problem by cracking the lid open just enough to reach in with my metal pizza peel, but still, time was working against me, and I couldn't afford any unnecessary heat loss. By the time the fourth pizza came out the thermometer was registering a paltry 350. Three-fifty's for baking cake, not pizza.
I did remedy the problem somewhat by finishing the later pizzas directly on the grates, over the dying but still-hot coals. That did give the underside some nice crispness and charring, not to mention some cool-looking grill marks. (Sorry I neglected to take photos, but I had my hands full making the pizzas. My 6-year-old daughter took some, but although she faithfully copied my methods, right down to photographing the undersides, her 1-megapixel Kidizoom camera doesn't exactly produce sharp photos.)
The results here were good enough for me to try this again, but my thought for next time is to try feeding the fire with wood chunks as soon as the coals reach their peak. I'll still start with charcoal because it burns longer than wood, but adding fresh charcoal during the baking process might give off some nasty chemical odors. Since my grill has a side firebox, I can feed the wood in through the side opening. I'll let you know how it goes.