Sorry your first try at grillin' pizza didn't turn out, Ed; coincidentally my missus and I did grilled pizza today and it turned our perfect. In fact, I way over indulged and and now stuffed up to my eyeballs!
However, I'm using a gas grill, and it is turned down to as low as it goes - here's the unit with a cooking pizza on it (click the image to enlarge it)
Notice that the crust is directly on the grill - first the raw dough was painted with olive oil and then placed oil side down directly on the grate. Once the crust was done on that side, it was turned over to the point where you see it in this image (you can see grill marks) and the toppings are loaded. The raw side of the pizza is down on the grate at this point and is cooking. Meanwhile, the side my wife is loading is piping hot, and toppings starting to cook as she is loading the crust. If you look close you can already see the cheese melting.
Here's the finished product - crust is almost cracker crisp, no trace of burning on either side, and the cheese is melted and tomatoes cooked through (the tomato slices were relatively thick).
I've never tried cooking pizza in a cast iron pan so I can't offer any advice, but one thing I would recommend is that if you try the charcoal grill again, next time fire the crust directly on the grate, and use a much smaller fire - something equivalent to the heat produced by low on a gas grill (sorry, I just don't know enough about controlling charcoal heat).
The wood fired oven is an entirely different story - it is true that the fire is scraped to one side of the chamber, but it is not the direct heat from the coals that is cooking the pizza. In fact, if you build a fire in the oven and immediately start cooking, you'll end up with poor quality pizza almost guaranteed (I made that mistake and learned my lesson). The way the oven works is that the fire is built at least a few hours before you plan to bake the pies - the heat from the continuous fire is being stored in the thick walls and floor of the oven so the entire unit is uniformly radiating heat toward the center (that's the reason the dome shape is such an advantage).
Sometimes I fire my pizzas at 900F plus/minus a hundred or so degrees (my thermometer only goes to 900F), and the side of the crust farthest from the coals cooks as quickly as the side that is next to the coals. Check out this image: the fire is to the right of this pizza, yet the opposite side of the pie (left) is cooking just about as fast as the side closest to the fire. (that pizza was done in 90 seconds)
