UPDATE. Made some suggested modifications.
I tried it again this Sunday. I made 3 modifications from the last cook:
1. Raised the pizza stone up on 2 refractory bricks (so it is maybe 1.5 inches higher)
2. Moved the stone all the way to the front of the oven
3. Added foil to the inside of the lid
Bonus: I also took the advice of several and kept the volume of toppings down
This worked a bit better than before. I was not able to get browning on the cheese in the oven, but it was getting close. I still finished them under the broiler. I had a little bit of trouble with the foil - a large bubble formed and stuck to it. It happened a second time after I fixed it, so for the last pizza, there was no foil - I just got rid of it. I also think i had the lid off too much on that last one, or it might have turned out even better. I was a little gun shy on burning the crust, so I was checking it, so maybe things would've worked out better if I could keep the lid on at the end. I may still be trying a new, smaller stone.
Don - UDS | Weber Kettles rescued from craigslist