I am no expert here, but have been trying to understand this issue so here is what I know. To begin , I have a '95 Sahara with the stock aluminum wheels running the exact same tire as you. They rub! They rub on the leaf springs when turning the wheel all the way to one side or the other such as when parking.
Now what you don't say is what wheel size you have and that matters. I will assume you are running 15X8, but the numbers change depending on whether the wheels are 8" or 10.5' etc.
First a couple definitions: There are three basic offsets, Negative offset, positive offset, and zero offset. Negative offset is the when the mounting surface is closer to the center of the jeep compared to the wheel centerline. Positive offset is the opposite, and refers to when the mounting surface of the wheel is farther away from the jeep than the wheel's centerline. Zero offset refers to a wheel that is neither positive or negative offset. The mounting surface is centered in the wheel.
Rear spacing or back spacing is the distance from the backside of the wheel mounting plate to the outside of the rim flange (bead). This seems to be the more important measurement when shopping for rims but the two measurements are tied as follows.
Assuming a 15X8 wheel, a -12mm offset should equate to a 4.0" back space, meaning that from the back of the wheel mounting surface to the end of the wheel (outside bead lip), 4.0" of the wheel extends toward the center of the jeep. Of course the tire when mounted extends past the wheel.
I am told that the stock wheels I have, have a 5.5" back space which equates to a +25mm offset. As I said, they rub when turned to the extremes. I am guessing that I need about an inch more of clearance so they would not rub. If I stay with the same tire size, I would want a 4.5" backspace at a minimum. With a 15X8 wheel, that would equate to a 0 offset, meaning the internal mounting surface is installed in the centerline of the wheel.
So if you think you need to increase your back space, i.e. tuck more tire inside the wheel well, the only option I can think of is to get new wheels with greater backspace. You have 4", you could go for 4.25" (-6 offset) or 4.5" (0 offset). Anymore and the tires will likely rub if ou stay with 31X10.5 R15 tires.
I don't know if pushing the tires further away from the centerline of the vehicle puts more strain on the drivetrain or not? They certainly sell a lot of wheel spacers for guys like me that need less backspace to stop the rubbing on the frame or whatever and don't want to buy new wheels.
Again I am no expert here and I am not positive of the offset on my stock wheels, but that is what I have read. Also again, if your wheel size is something different, say 10.5" and not 8", all the numbers change. For instance, with a 10.5" wheel, -12mm offset equates to a 5.25" backspace instead of the 4" backspace on a 8" wheel.
Hope this helps.