I can't necessarily give you the rundown on specs that will/won't fit and where the cutoff is between, but it looks like our setups are similar, so I can tell you what works with mine, which should work well with yours or at least give you a data point.
I have a 2.5" lift on my TJ and am running 31x10.5 on 15" rims with 3.75" backspacing and get no rubbing in any scenario. I'm currently running Kelly Edge ATs and I've been happy with them for the most part. They're a mild AT that does great on-road and fine off. When I need to replace, I'll be moving to either the BFG KO2, General Grabber or Toyo Open Country AT3 as these have a heaver duty sidewall than the Kelly's (3-ply vs. 2), which is important with all the sharp rocks we have here in the desert.
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