On my 2000 Sahara with Canyon wheels the backspacing was 5.5 inches, its hard to find any aftermarket rims with more than 4.5". I ended up getting some Dick Cepec 15x8" rims with I think 3.75" of backspacing which put the wheels almost 2 inches farther out. I was worried about moving them that far out, but it ended up looking great. I'm running the same 31x10.5 tires as you.
I think the Sahara flares are a little wider than the stock flares, so you might look at something closer to 4.25" of backspace if you don't want the tires to stick out.