While there are areas of the 38A that require specialist knowledge or equipment, I think you proved, by your comments about the GM specialist you know, and perhaps trust more than the Land Rover dealer, that the drive train is an area where you can give work to the GM people.
You say you have tried new drive shafts, with a 50% improvement. By 'drive shaft' you mean the shafts between gearbox and axles? I ask becuase in the UK they are propshafts, in the USA they are drive shafts, and I want to make sure confusion is minimised. (In UK English, drive shafts tend to be the open shafts (gearbox to hub) used for front wheel drive cars, or rear wheel drive cars (differential to hub) with independant suspension. Shafts inside axle tubes, as the 38A's live axles, are termed half shafts, in UK English).
You are chasing a vibration: the first point to look at is the Universal Joints in the propshafts (both propshafts), these can be loose (worn), or tight (almost seized) and you have to unbolt each joint to get a true assessment. From your comments, I assume you have changed these.
The auto box does suffer from a cracked flexplate, but this would have become apparent, I think, in the 180 degree move you had done.
Don't forget the obvious, of a tyre defect, or out of balance.
Wheel bearing is possible, but I think you have discounted those.
CV joint in the front drive shafts? Possible but unlikely.
Have you compared your car (now you have changed the propshafts) with another 38A?
If you do change the differential, front or rear, go for the 4 pin ones from Ashcrofts. There is no setting up, it's just pull the halfshafts / driveshafts, unbolt the old, bolt in the new, fill with oil, and that's it. Easy money.
There is more work if the old diff has left a lot of metal behind, in which case you need to make up a swab, of paper towel around a broom (brush) handle, and wipe out axle tubes, pushing and twisting from the wheel end towards the axle centre.
It's still easy money though.
HTH