I was also told by ineos driver that you can lock/unlock centre diff on the move, when i was on a test drive. However, it doesnt make intuitive sense, not because of the transfer case, but because of the torque converter pushing or braking.
on all defenders I can absolutely do this at any speed, providing the vehicle is not turning a corner or wheel spinning at the time, ie the centre diff is not absorbing differential rotations. And you momentarily depress the clutch.
you can not change ratios under way without problems, as stated by others there is no synchromesh. Applies for up or down. Very slow movement I still dislike, better to briefly engage the clutch in the transfer case neutral position, that re-positions the cogs for enmeshment.
im not clear if the grenadier has a defined neutral position for the transfer case, i think not. But, as it has no PTO, and does have an automatic gearbox, there is no real need for it.
I think the cnetre lock on the move is probably a casualty of the automatic gearbox, which, on balance, I feel is probably worth it. 20 years ago definitely not, but these autos are brilliant, and this is not a 20 year old design - happy about that!