I'd imagine a lot of use use locking hitch pins which are a bit longer than the tiny pin your using, and would cause interference.
yeah, the biggest issue would be getting it in there. i'd have to measure mine, but i don't think it would clear that tight space. that said, other than widening the 'indent' where the hitch is recessed, there's not much i can see to correct it that wouldn't sacrifice departure angle. either flush mounting it below or extending it out past the bumper both cut into your angle.
Luckily most of the damage was to just the bumper cover with only the lower wing of the quarter panel under the bumper cover getting pushed in a little. Should take care of about half the cost.