That type of oven control is typically ON/OFF, not proportional.  Not only will you need to be concerned about overshoot, that kind of controller typically relies on having an effective pilot light.  If you are going to use an oven controller, you may need to use the entire gas train hookup, including pilot safety system.

I think it would be less effort and a better end product to use the guts out of a toaster oven and an inexpensive PID controller.