Not saying I would advise it and not endorsing this kind of nonsense. But if I tell someone I'll help them out I do my best.
Buddy in MD wanted some wheels/tires that were 60 miles below me in VA and he is 60 miles above me, that he'd found on Facebook for his p/u. Anyways short story he couldn't go and the guy said he was going out of town. OK whatever so he asked me if i mind and he would've done the same for me so I said sure. Kinda forgot other half had the pick-up for ball and all I had left to stuff anything in was the Jeep. No biggie, hop in went on my way. He told me a set of 35's on 20's but I guess it didn't really register. Grant it I'm only maybe 2 months old owning a jeep and only other 4wd I've owned was a small blazer many years ago in myrtle beach which I only used a couple times to get my dum azz out of the sand.
But I show up to pick up these tires and this guy has a full size Ram with the bed spilling over with these monsters compared to what I'm used to.
He looks at me and says I think your gonna need a bigger Jeep or were throwing a couple on the roof. But after a couple quick looks and mental calculations I thought there just might be a chance. Once 1 went in flat I knew we were golden. And 3 rode flat stacked in back all the way home till I turned in driveway and the top one slide over. I'm not sure what they weigh but I can assure you there not light by no means.
Other I got to line up 1 stud on spare tire carrier and it sat nice and flat on pad crank a lug not on it, mad good contact on a couple bumpers iirc. put a ratchet strap through spokes and around carrier and it was good. Snug fit really didn't have a bunch of bounce which i was thinking because of weight. Rode good.
So I would say a 31x10.5x15 should be no problem at all for as long of a haul as you want. honestly I wouldn't be afraid of 32/33's possibly. Cause that 35 is on a 20" hunk of metal also. But as I said I wouldn't advise anyone to do it with a 35 but 32/33 I would say wouldn't have a problem. Again as everyone has said have good rubber too rubber contact with those bumpers, and all 3 lug nuts is strongly advisable.