You could try a 295-70 r16. I currently have 305-70 r16's on my 2500 and they clear ok. The 2500's are higher than the 15s though. You'll basically need to stay smaller than a 33" tire.
Mike,, You'll find several Options, just make sure of your Clearances both Height and Width before going to big!!!! With that sd, in a LT285/75R16 or a LT305/70R16 or a LT315/75R16
youll have several Choices to Look at all with a D ply Rating