I know exactly what you mean. Hard to focus/coordinate your hands and foot both while doing something different with each. Sometimes I go faster and faster until I lose control. And since your Jazz has no electronic speed control, it would naturally be even harder.
The idea of taping something to the pedal to limit the movement until you get the practice hours in is certainly a possibility. I also wonder if an electronics/electrical shop can sell you something that allows you to adjust power coming in to the machine. Years ago we had these little boxes that you could plug a lamp into that allowed you to increase or decrease the light. I think it was a simple rheostat control. This would not be good for a computerized machine, but for a purely mechanical machine it might work. Perhaps inquire at an electronics shop or electrical supply store if something like that still exists and if it would be appropriate on a mechanical machine like this.