The main issue is heat control. You'll want to do it with indirect heat so you don't scorch it, but you'll also want to do it with more heat than indirect heat usually generates.
This is how I would figure it out.
Go buy some oven thermometers.
Now set up your Weber as you would for cooking your Wellington. Probably two banks of coals on opposite sides depending on the size and configuration of your Weber.
Place the thermometers on the grill in a line from from bank of coals to bank of coals. Cover with the lid. Check after a bit to see how the temperatures vary. It can take the Weber up to 15 minutes to reach it's stable cooking temp every time you remove the lid. However, you also want to know how the temp at the cooking grid varies by location, not just the average air temp in the Weber.
Air temp and recovery also varies with local conditions such as temp, humidity, direct sun and so forth. That makes this some trial and error until you get a knowledge of your cooker in various conditions. That's why its important to write things down so you have a reference to help you cook the right way on the day of the competition.
Make a diagram of the Weber and describe the coal number and placement. Also record weather conditions. Now mark the temperatures on the diagram. Repeat with varying locations to figure out where you'll want to cook your pastry. You may have to try different coal configurations to get the temperature you want in the position you want.
Figure on rotating the pastry dish during cooking as it will probably have hot and cold sides you will have to even out by rotation every so often.