Since no one else has come up with anything better, I'll chip in with my limited experience here. When I had a round eye LJ70 I ran 31s, like you.
On my current KZJ70 the body and chassis are very similar to the earlier LJ but I'm not sure exactly what the differences are in detail. When I put 33s on it there was no rubbing on body or chassis, but I had to cut and re-weld the exhaust downpipe to move is rearwards a tad since the tyre touched it on full lock. But that was after a 50mm suspension lift, so this info is not really much help to you. In short, I would be surprised if you could put 33s on without having to get involved in some mods.
Having bigger tyres is a major improvement off road in the rough stuff. Bearings, brakes and gearing can all cope long term with no downsides at all. And, of course, they look a whole lot better. But here's the surprise - fuel consumption is slightly worse. Since I put 33s on I have never been able to match the mileage per litre that I got on the 31s.
You're not a million miles away. If you are ever in the SE London area get in touch and we can stick some 33s on your truck to find out.