Sounds doable. Will try to give it a shot.Sheet metal screws and mine is better than new. Cheap design by ford, they should know better.
I assume these were pointed screws, bolted all the way thru the plastic frame to the backplate on the seat assemble. Can you tell what length screws you used.
Maybe be better if we remove the carpet - if it is doable , drill down the screws and paste the carpet over it again to look more neat. A thought anyways.