FIXED!!!
I was distraught over this. It was disgusting. I didn't even want to touch it. Using gloves, I took the whole thing apart (pretty easy, actually, just a lot of screws and ribbon cables to be careful with).
I sprayed and covered the whole exterior with Goo Gone - this, specifically:
https://googone.com/goo-adhesive-remover-spray-gel
I did two rounds of this, letting it sit for hours each time.
I rubbed it with a durable paper towel, and it's fine. Don't be idiots like me, and get it on the screen, though I can still see..