Biggest issue I found was it seemed like the cover had shrunk a bit when I reinstalled it.
As too my initial problem, the answer came to me early the next morning when I realized that the 'screws' I was afraid of stripping were actually those funny fake screw/rivet things. They took a bit of damage removing but I can live with it until I get around to replacing them. When they replaced the damaged cover when I bought the truck, they didn't exactly replace them in pristine condition either.
But long story short, for $16 I got the trailer wiring harness from my dealer installed and now I just need to pop in the relays and see if it works.