In my experience, gearboxes, propshafts and diffs whine or grumble rather than shake the car. This is because they're revolving at several times the speed of the road wheels (depending on the diff ratio).
If you can feel it through the steering wheel, then its probably front wheel related - tyres, rims, brake disks, shox, track rods, ball joints, centre tie bar.
If it's shaking the whole car equally, then rear wheels are more likely - so rear tyres, rims, brake disks, rear shox.
I've got two stories related to the LC. First one was a vibration under light braking through the whole car. Turned out to be one of the rear brake disks (which are vented) had cracked in the venting. This allowed the two halves of the brake disk to spread apart slightly. You noticed when you first applied the brakes lightly, but it would stop under heavy braking (because the two halves of the disk got squashed back together again). Then on lift off the vibration would continue for a while until the pistons/pads had been 'knocked back' far enough so as to not hit the brake disk. AIUI the 2.6 has vented rear disks? Might be worth checking the run out on both the inside and outside faces of the two rear disks.
Second story took me several years to locate. On hitting any sort of pot hole the steering would vibrate quite violently for 10-15 seconds. You could stop the vibration with a slight dab of the brakes. I'd replaced most of the front end of the car - Wishbones, track rods, brakes, brake disks, shox, top mounts, drop links, roll bar bushes etc. Nothing fixed it. Then finally I'd decided to replace the power steering box, and to do that I had to take the centre steering tie bar off. The ball joint in that was rubber ducked.