Congrats on doing the skirts.
It might net you some cabin noise-reduction too. I highly approve of using flashing, my material of choice. And cool that you can change the tires without removing them! Very handy.
You can probably get away with fewer mounting points than that on the edge of the wheel well too (would link an example pic but don't want to be spamming your thread with pics
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Plastic and foam aren't a big problem. I've got a short airdam + undertray attached to plastic that lasted five years without a single screw coming loose. 25+ sheet metal screws (I use slotted hex washer head sheet metal screws with as deep a thread as I can find), and the undertray keeps the airdam from bending back. Roommates have hit a curb a couple of times and it stayed firm, I just bent it back in place, and the new one I just did on my second car, I can push on the bottom edge of it and rock the car back and forth (automatic in park).
If the plastic is _really_ weak you could try drilling the holes while wiggling the drill around so that the hole widens the deeper the hole goes, fill it with some sort of filler/rubber/whatever, then drill into the plugs you just made maybe? Dunno, just pontificating.