I’m sure this is sort of a dumb question, but can I just solder mechanical buttons to the contacts on a membrane button? As I understand it, that would still complete the path.
Membrane keypad would have 2 issues that would prevent it, first the membrane is most likely not heat resistant like flexable PCBs and would melt if you tried to solder to it, second the black traces on the membrane are made of powdered carbon in a binder and would not take the solder or would break apart. You could use a pressure fit to hold the contact of the switch to the traces if you where somehow able to hold the switch in place.
The few items I have in mind have hard boards with a little rubber foot that touches either two half circles or two wiggly lines, though I do have one of those plasticy ones you’re taking about. What if I trace the lines back to the board and replicate it with wire?