I found a nice gear calculator on www.izook.com I think the 4.62 gear ratio should work well for 31" tires.
I have a set of 4.625s in my 1.6 8-valve Samurai with 30" BFG ATs and the change from a DD standpoint was amazing! Better mileage through a better matching of the engine to the drivetrain. I got 5th gear back and I almost never "row" (downshift) to keep my speed up on the Interstate. Because of the R&P swap, I don't load or stress the engine and drivetrain as much as I used to.
Yes, I am a big fan of R&P swaps.
But to be fair, rebuilding two Samurai dDifferentials with Trackick R&Ps involves a lot of detail work and - to make sure that you don't have to crack them open again soon - two rebuild kits. Re-gearing the transfer case can get "nominally" the same results for a lot less physical effort. The engine/drivetrain loading mentioned above ends at the transfer case instead of at the differentials. And there is where the debate begins.
I, like Descarte's vision of Godhead, have wound up the Clock of Predestination and walked away. Let the discussion ensue!