To tell the honest truth, I was thinking jeepeater had a fairly stock rig (no I didn't look at his profile- until now), that is what I suggested the 1" .156 wall. But having 39's and whatever else he had listed, no I would not use anything smaller than 1.5", .250 wall. As for the traction bar, he should probably use something larger just because the size of the rig, but I do not see that something in the 1-1.25" OD, that was .156 (for 1"), or .120 (for the 1.25") would be too weak for a smaller rig (like mine). I and a friend used 1.25" .120 square tube, and with a brace in between the two bars, and the lower bar running as far forward as possible, IMO that is plenty strong enough, you can give me your calculations all you want, and when I break it I will tell you that you were right.
Also, being in a racing program, I am thinking about the trac bars being straight, not like what is normally on a Jeep having a couple bends in it. 1" .156 wall is PLENTY for a straight traction bar, heck you could even use aluminum. Tell me going around Daytona at 195 MPH doesn't put some load on a trac bar, somehow they get by with the aluminum ones or the steel ones (not sure what NASCAR uses) but I bet if it is steel it wouldnt be thicker than .156).
Put a bend in the bar (which would probably be a must-have), and I will agree 1" .156 wall would not hold up.