Has anyone seen or used any mounting kits to change the position of the front license plate?
I would love to move it away from the front grille, possibly lower and/or to the side of the car.
I have not, but another thing to consider is that if your car has the tech package, the radar for the cruise control is in the Hyundai emblem on the grill. That emblem becomes the furthest protrusion on the front of the car if the plate holder isn't mounted under it. I'd be very angry if a small tap from a parking job resulted in that emblem getting dinged and possibly damaging that sensor. I am sure it would not be cheap to replace. Having the plate there provides a little bit of protection.
I don't have one personally but I have seen on a couple of Facebook groups that people use a tow hook mount. I didn't search again but I am pretty sure it was one for the Veloster that fit both the GT Sport and the ES Sport.