Not sure if this is close, but did the 11 Rubicons have that tinfoil little cross bar that my 14 did right under the exhaust up front (I have no idea what Jeep calls that part, just a thin metal bar, not the transmission crossmember and it certainly wouldnt qualify to be called a skid)? I had a similar noise on acceleration. I had clunked that bar on the trail and the exhaust was rattling on it. I solved the problem by getting real skids which removed the bar.
2014 JKR "Bob" - RK X Factor 2.5, Nitto Trail Grapplers 37x12.5x17, Auto, 5.13, Rock Hard Skids, PS HD Cross member, Artec Axle Armor F&R, Artec Rear LCA Mounts/Skids, Synergy Rear Axle Side Weld on TB Bracket, PSC Hydroassist