If the treadle does all the mechanics, wouldn't limiting its length of travel do the trick?
Figure out (direct measurement I would guess) how much you need to limit the travel and put a block of wood that thick under the treadle.
Push it all the way down and then back off until you see the nail head is flush with the bed and have someone measure from the underside of the treadle to the foot's surface. (The screw holes in the foot may be a clue to a missing part that is involved with this).
There is probably some kind of mechanical adjustment to achieve a better result, but seeing as the machine is a temporary backup, why not quick and easy?