The US plate Lambo bracket(have it) for the H sucks,it is not correct as the Hs are made for Europe plates.I almost had the same issue as you have,but have it screwed in ok for now.Yes,you can only use two upper screws and their is no were else you can put the Plate on the H.Future Hs should be redesigned to accommodate US Plates.

Above solution is probability best...