You could get a 4x5-inch Graflex (or similar - something that leaves you in charge of the bellows extension so you can adjust it for a shorter-than-normal lens), and put a 6x12 roll-film holder on it, and a lens that doesn't quite cover 4x5 - something like 5 or 6 inches, intended for a 3x4 Graflex - to give you the darkening edges. You probably won't find this lot already assembled as a kit. I suspect the film holder would be the most expensive bit.
If you make the camera a Speed Graphic (with a working shutter), then you can try lenses without their own shutter, which will be cheaper. You could try enlarging lenses, projector lenses, anything you can mount up, and find the level of 'badness' that satisfies you!