Tires are the RRS's white whale. I have a 2013 RRS with 20" rims and have spent countless hours figuring out the best fitment for off-pavement travel. My conclusion: 285/50R20 is the optimal size and the largest tire you can fit without significant rubbing. That size gives you a diameter of 31.3", and has virtually no rubbing (only a tiny tiny amount of rub at full lock when reversing). 275/45R20's are another good option -- zero rub, but you get less tire. I haven't tried them myself, but the consensus from many RRS owners who have is that you can fit 275/55R20's but you'll have a fair amount of rubbing, even with a lift.
There are only two all-terrain tire options available at the 285/50R20 size. Cooper Zeon LTZs and Nitto Terra Grappler G2's. I'm on my second set of LTZ's. I got Cooper to warranty replace the first set after a bit more than a year of hard use off road that chewed up the sidewalls and resulted in one tire experiencing a blow out over some sharp volcanic rocks. I don't know if this is a general durability issue or just a bad batch combined with my abuse. Apart from that, the tires have been fantastic both on road and off.