Just guessing, but seems to me you could convert the webber to an old-fashioned hearth oven.
In the old days, a fire was built right in the oven, to preheat it. Then the coals were shoveled out, and the baked goods put in. Seems to me you could replicate that with bricks. Fire bricks would be ideal, but even regular construction bricks would work. The idea is to create thermal mass to hold the heat in.
After the meat is ready, put a few bricks on the grill to heat. Prep the meat, wrap it in the pastry, and return it to the "oven."
You'll have to experiment to figure how many bricks it takes to reach, and maintain, baking temperature. And you may or may not have to remove the coals once the bricks are heated. Another possibility is to use a pizza stone (or even a large terracota dish) as a tray to hold the meat while it bakes, for additional temperature control.
FWIW, the terms "Fast, Medium, and Slow Oven" now have precise temperature equivilents. But in the old days, before thermometers were common, you determined this by putting your arm in the oven. If you could hold it there comfortably for 20 seconds it was a medium oven (about 350F). If you couldn't, it was a fast oven. And if you could hold it there longer than 20 seconds, you had a slow oven.
