drill ~10 small holes, ¼ to ⅜” diameter, inside that rectangle (location isn't important, a random distribution is fine)
run ~12 gauge steel wire into one hole and out another
Hopefully it's possible to mostly avoid the headliner material with these wires. This isn't 100% necessary though. However, definitely avoid any internal wiring routes.
(optional) twist pairs of wires together, tight, to make sure all wires are seated high against the sheet metal
Or…. run a single continuous wire in and out, over and over, and then cinch the whole thing tight just like rope lashing!
Pour epoxy over the entire foot. This has two purposes: 1) to seal the holes to prevent water intrusion, and 2) to bind the separate wires together into one single mechanical support.