Hardtop Latch Repair

[pdx124]

I'm looking for suggestions on how to fix a latch that had the screws rust out, then the entire latch came off. Now the two holes are exposed but the metal back plate behind the fiberglass/plastic headliner is out of place. I cannot screw the latch back in with nothing there to hold it. I don't want to use tapping screws that will damage the headliner. Pressure from clamping down could strip them out, in theory. Luckily I've driven it in rain with no serious leakage thus far. The one good clamp is holding it down okay.