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.