So I think I understand why I am seeing side to side movement and associated noises and you (
@Bellfab and possibly others) are not.
I don't have factory carpets and padding, I have bare floors, no sound deadening and trufit vinyl floors. So... with a 35" tire and the support rod plate at the lowest possible position, the tire is still off the floor by fractions of an inch. I don't have the bottom of the tire pushing against the floor creating additional points of contact to resist sideways movement - all three bolted down supports are roughly in line parallel with the direction of travel.
Now this would be ideally solved by having a revised version of the mounting plate that allows my 35" tire to touch the floor.
As a bandaid, I put a plastic spacer plate underneath and a lateral spar to the side wall. Not elegant, but we do what we have to. It stopped the movement and noises.
I'd be more than happy to try a new mounting plate that would allow my tire to rest on the floor.

Let me know.