Quick model of "Pin Fix" hardware.
Existing mount that the pin would stick up from would have to be drilled with about a 1/8" hole (larger would be fine as there is often a larger hole where the pins break off).
The flat area of the mount that the pin stuck out of would be sandwiched between the pin section and the washer section, then tightened down with a small button head socket screw.
Would probably be stronger than the original pin I think. Probably an hour on the lathe to turn up a couple of them.
(for scale the OD of the washer is 1/2")