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Not sure what your budget is but if you are interested in going up a sizeI have 285 65 20's (BFG's)on my 05 Ram and they don't rub at all. Quite pricey though (over 300 a piece)
In 275/60-20, the Bridgestone Dueler Alenza and Michelin LTX are probably the two best that we have at Tire Rack. 285/55-20 works as well. You can get the BF-G All Terrain T/A in that size.
I've got LT305/55R20's (34" x 12") on my 2005 Ram 1500 SLT Q/C 4x4and are good enough for the stock height. If you go with 35"s, it would be tight for suspension travel.