We are building a new home and the transition from the tiled foyer to the family room, dining room, living rooms to be carpeted is l 1/4 inches. The carpet installer says the gap is too steep and will require shims throughout the perimeter of the carpeted rooms but that we might feel the incline/transition. Builder says he never drops the subfloor to install tile anymore, and did not drop our floor for tile install-suggests we can just use a thicker carpet/pad.and the shims--our expense. Any ideas? My husband wants to put more plywood down on subfloor-obviously a pain to do but we don't want the sloping.