An early Mamiya C series TLR body would do. Only 6x6 without Polaroid (there are some drastic modifications along that line, though), but you do have a sports finder which can take masks. The bellows would give you a pinhole to film range of about 80mm to 135mm (a 'zoom' pinhole!). The film change baffle inside the camera will allow safe film advance. The pinhole mount is a simple plate to fit over the lens opening.
The shutter needn't be anything more elaborate than a piece of black tape. At around f256 or so the exposure is not going to be less than 1 second.
Any Press camera or a 5x4 with roll-film back will work, too. It does pay to have the larger format since the unsharp images suffer if over-enlarged.