That cutoff lever looks ok unless the lug for the spring is missing; I doubt that you will be able to get a replacement for it. You might be well advised to replace the gearbox; if you do, I would make the standard recommendation of fitting a Perun Hybrid.
Regarding the overheating, If you do not replace the gearbox, I would advise replacing the wiring, as well as checking the shimming. Any two lug QD spring guide should fit, albeit possibly with a little filing of the lugs.