While I have used something as simple as DAP Contact Cement on a replacement Foam Pad on a Craftsman Orbital Waxer, this type of Glue would probably not be good enough for a DA or Rotary Backing Plate which likely sees more heat, and possibly liquid chemicals.
I might lean towards using a 2-part Epoxy that can stand up to such rigors, and perhaps something like JB Weld would work fine. Once mixed, one should be able to spread a thin amount where needed, clamp with some pressure or weight, quickly wipe away any excess and let fully dry.
JB Weld is easily gotten, wally world and such, just see what it can be used on before buying.