Sorry. I’m not convinced. Where did the extra rubber go? Why don’t we recalibrate our speedometers for heavy loads? The axle is closer to the ground. But the distance around the tread has not changed. We just Chang the shape from round to “D”-shaped. That measurement from pavement to axle is not a true radius because we’re not talking about a circle. If you measure from the axle to the top of the tire, you will find that the radius has not changed.
(BTW, circumference = pi x diameter)
Where does the extra rubber in the sidewall bulge come from? Answer - from creation of the 'flat spot' due to weight of load. And if mathematicians were creating the speedometer they would want load compensation, but engineers are fine with "close enough for practical purposes." They design the speedometer to read within 1% at the average load with the stock tires. So, yes the axle center to pavement is the radius you should be using and circumference = pi * loaded radius * 2.
Aside the flexing the tire to create the "flat spot/sidewall bulge" is what creates heat in tire.
Finding 4 identical tires on the rack is nearly impossible. Given a 30" tire rotates ~675 times/mile, a .05" difference in radius results in dragging a tire the length of the truck every mile if you don't have differentials (either in axles and/or transfer case).
Back to the original problem: The planets in the low range gear train, turn at more/less the speed of the reduction. I.e. 2.48 * input speed. If input speed is: Engine 4,500 rpm / .75 for OD, the poor little planets are spinning ~15,000 rpm!
It has historically been a issue with Jeep Rubicons: Their transfer case has 4.0:1 reduction, so when people forget to shift out of 4lo, and attempt to drive highway speeds, their planets spin up to 30k rpm for a few moments, then there are all sorts of transfer case pieces on the pavement.
I would check the oil in the transfer case to see how badly heated it was. If it smells burnt; you need to investigate further.
And who reads manuals??