I'm sorry Mike , i wasn't discounting your diagnosis , i was actually just adding to check the simple things first . I would certainly recheck the tyres first , as a speed related wobble can often lead to something as simple as the tyres themselves .
However i do have to diverge from your advice , despite it being good advice as usual , something i would expect from an ex -professional . I personally , would be extremely worried about jacking a 3 ton vehicle up , and turning the wheels at high speed using an engine . That is to my mind is an extremely dangerous thing to suggest to any amateur . You have no idea of the posters capabilities , (no offence intended to the poster) , and is well outside the average weekend spanner whirrer remitt anyway . I know you have emphasized how you would go about this , but the average home mechanic has inadequate equipment to even jack these vehicles , let alone what you're suggesting . I know i don't , despite having an extensive tool kit , and the correct jacking and support systems for my own Motorhome rated at 3100kg empty . The handbrake (which incidentally is notoriously inefficient on these vehicles) would never hold it back , and should something go wrong with the vehicle falling off the supports . At the wheel rotational speed needed to show this fault up , it would move a significant distance in a very short space of time (seconds in this case) . There a very high risk of serious damage , or injury being the result .
Sorry Mike , but i can't endorse this particular course of action , and you can rest assured , that is from someone that has a very low opinion of the health and safety executive .