Oh wow! No, they don’t make the Cooper in a C load for 35x12.5r17. You’d have to go to a 40x13.5r17. I’m sure you eventually will get to that size tire.
I know, it blows my mind, especially since the JK guys are all running 17s, yet the only one to offer a C load tire is Goodyear? Makes no sense. 40s... haha. At that point it's a dedicated trail rig, I'll say that much.