I really like the look of it. Compact, stylish and looks like it will last forever. Minus the baking surface, it looks like what I'm familiar with as a "chiminea".
However, as you said, you could do a few things to improve your top heat, and attain the leoparding you like.
1. Install a damper on top of the chimney. This could be as low-tech and ugly as inverting a large can with holes punched in it over the top. Or you could get fancier and buy a nice-looking chimney cap; that will cut the exhaust flow substantially.
2. Create a hinged metal door that can mount to the top of your opening, that reduces the opening size by about half. Hire someone to do this if you don't have access to the right tools. Open it all the way to lay the fire, close it to reach your desired top temp. Leave it closed when baking. You should still have plenty of vertical room to launch, turn and recover your pizzas.