My 15x7's don't play with the beauty ring well. It's like they welded the centers in backwards. The hoops of any wheel have a taper on one side and a fairly sharp bend on the other. The sharp bend is on the outside and screws with the trim rings I have. May be those "deep dish" rings would take care of that.
I don't recall how mine looked without the rings. Maybe they goofed on yours? As you can see above, the 3" rings fit nicely. They were hard to put on. It took two sets of hands.