The only way I see you consistently being able to do this with the equipment at hand is to pre-cook the burgers using the toaster oven, then zapping them real quick in the microwave to order. For example, say you open at 11am for lunch. Start pre-cooking at 10am and keep them in a foil covered hotel pan or aluminum foil pan. When you get an order, nuke it for about 30-40 seconds. Depending on the volume that you'll be doing, only pre-cook enough to where the burgers will be at room temp. for 1 hour tops. If you're busy, you'll be constantly pre-cooking throughout the day. Make sure that you properly rotate the burgers (FIFO - First In, First Out) and switch/wash pans every hour as well. If you plan on doing these burgers to order there's no way in h.ell that you'll be able to keep up with just a toaster oven.
"Boldness has genius, power, and magic in it."
Johann Wolfgang Von Goethe