I've never been in a differential but I know there are bearings that could wear out. I noted them when I was reading the FSM about the shaft. I too worried it was a bearing, afraid that it had been driven too long with a wonky shaft. But being an LC I'd expect that as long as it's generally been mostly properly lubricated it should be fine. Someone else can speak to this better than I.
My thinking was that I can spend 2 hours crawling around scratching my head or I can be putting in new u-joints that I'll eventually need anyway. At their age and mileage may as well.
Just be sure to watch that Australian guy's video on YouTube. Press out one side and then grind it off, as in the video. Otherwise the shaft can be ruined. I did exactly what he did and all went smoothly.
I was just driving and thinking about your issue. I've got BFG KO2 285's and they definitely make a rumble above 55 or so. And I started thinking that with the tires and wheels the size you have definitely gives more room for manufacturing errors and then if the balance shop doesn't put in much effort that could do it. I've also heard about tires with slightly warped belts that don't affect balance but do vibrate when driving. Doesn't match your symptoms though, I think ithat would be noticeable at all speeds and would increase with speed.
While I was chasing down my problem I stopped by a shop where I know the guys. One of them is an older guy and a real "car whisperer", although not an LC specialist. I described my vibration as starting right at 65mph, increases under acceleration, and after a few seconds it decreases when I let off the gas even if still over 65mph.
Shop owner shout out "wheel bearings" but the car whisperer whispered "what you just described is u-joints". I told him that I thought so too and told the shop owner that the front wheel bearings and races are brand new and the sound hasn't changed.
We put it on the lift and the mechanic went straight to the rear driveshaft u-joints. Pointed to the bottom of the caps and said "there you go". I didn't see anything, a little grease. He said that he sees wear and that's where it shows. I asked if it's enough to cause that vibration and he said definitely. There wasn't any play anywhere.
I replaced the front u-joints because they had been replaced by the previous owner and were obviously aftermarket. I had already looked at OEM and aftermarket joints and the difference in weight and quality was night and day. I assumed they could also lack the balance and durability of OEM so I just changed them out too. LC's really don't like aftermarket parts and I don't either.
My local dealer cost for new shafts was about $400 for the rear and $380 for the front, as opposed to $80 and $70 each for just the joints (x2). I enjoy the work but consider new shafts if you have to buy a bench vise, grinder, torque wrench, or if your shaft is otherwise worn/rusty or someone else has previously been in there and messed up the pressing or alignment. And also your time value.
Mine went quickly and easily. And rewardingly because it fixed the problem. Be sure to install them so that the grease fitting faces the right way, ie it's in the bigger opening. You'll see what I mean when you're there. Just make a note of it or take a pic during disassembly. Some people say to line it up with the yoke grease fitting but I put it opposite thinking about balance and the fact that no matter what it's position I should be able to get the grease gun on at least one every time I'm under there.
And be sure to mark the shaft for properly balanced reassembly.
It's a simple job but the details matter.
It's easy here on a forum to start throwing parts at a problem and miss. But this was my experience and I get so much from the collective knowledge here that I wanted to pass it along.