I know I said I wouldn’t contribute to this thread any more but here goes.
TPMS works by comparing pulses from the wheel speed sensors on each wheel - it doesn’t read the speed of each sensor, if it did it would go off if you went around a long corner or a series of same direction bends - it works by comparing the signals from each wheel looking for discrepancies between the wheels - imagine if you were sat on a half inflated football, it would feel squidgy and unstable - this effect modifies the signal from the soft tyre.
TPMS will pick up a couple of PSI, if you think this is because of a minuscule reduction in the rolling radius you‘re really not thinking it through. Try dropping 2 or 3 psi out of a tyre and see if you can measure the difference in rolling radius and then think about how much impact this would have on the circumference of 2m plus, the difference is minuscule - also think about when you set it - how would it know the rolling radius when it isn’t moving...
if you think you can accurately measure rolling circumference with a piece of chalk over 1 rotation - crack on but dont be surprised if you don't understand - IMO if the basics aren’t right you haven’t got a chance of understanding the problem. Also if you think you can measure it without the weight of the vehicle on it then you haven’t considered how a tyre takes the weight of a vehicle or how it maximises it’s contact patch.
With air suspension the van is much more softly sprung (isn’t that the reason people fit it) as such it will deflect in a completely different way (think less violently) - this will have an effect on the signal from the wheel speed sensors, if TPMS coming on is common on air suspended vans, I would bet the farm on the behaviour of the suspension being the reason.
A differential isn’t only about differences in driven tyres, its also about going around corners where the track taken by the outside wheel is longer than that of the inside...
Axle and wheel alignment can also have a big effect on fuel consumption and don‘t assume that your tyres are wearing ok so it must be ok. Think about a rear axle that isn’t quite at 90’ to the centreline of the van so the front wheels compensate to go in a straight line - this can have a huge effect and you wont even notice it - its very common on trucks and if you cant see it on a 13m trailer you wont see it on a T6.
We haven’t mentioned Ackerman angles yet