When towing at a steady 100km/h, I've found I get exactly the same fuel consumption in 4th as I get in 5th.......and a lot more noise.......so I doubt changing tyre size would save much juice. In 4th, EGT's were lower, and it's easier on the gearbox.
I had 285/75x16 BFG A/T's for many years.........couldn't kill 'em. I went back to 265/75x16 BFG KM2's for a while, but quickly went back to 285 KM2's, 'cos I can. I had a set of GU alloys with 265/70x16 Cooper ST's briefly, and I hated the short gearing. It was revving it's head off. Mine just feels happier with longer legs.....it's easy to change down if needed.
KM2's take a little more to push along than the A/T's, but it's more something I feel when driving, than I notice at the fuel pump.
Like BigJules says, I reckon you'll be disappointed with the 31's. Maybe give the muddies a miss, and go with 285/75x16 A/T's......