John, how much time are you giving the egg to heat up? Assuming you're giving an hour or more, I'd suggest checking the alignment of the firebox and the cleanout. There's always questions like wether the egg was cleaned out first (BTW, I don't clean mine, but little chunks of charcoal can clog the air holes in the bottom grate), the size on the lump (again little chunks can clog), dampness of the lump, etc, but seems like the most common issue is avoiding any restriction at the air supply.
To get the top of your pizza done faster, you have to make sure the egg is at the desired temp for some time before starting. IOW, if your target is 500, don't start baking as soon as it hits 500. You have to give the dome time to preheat. Your stone is thinner and closer to the heat source so it will heat up faster. Try giving it a good half hour AFTER it hits your target. If you're still having problems, try raising the pizza in the egg using something like a spider, putting the pizza stone higher in the dome.