Have you tried parking it with all the wheels off the ground to stop flat spots on the wheels
have said before elsewhere -- my 18t Grove TMS180 was so heavy on the front axle that parked up for any period the rims'd slip down in the beads and it'd be like driving on egg shaped wheels for several miles, 'til they sorted themselves out.
cured it by dropping the front jacks and taking the weight off the front wheels if parked for a couple of days. think the OP would notice, if this was the issue, from the off though
IMHDO it's more to do with the un-sprung nature of the beast and it hitting a particular 'spot' where it just 'does it' ...
the very short wheel base of a Hydrapig (and similarly the Rapier / Fairy) - nigh on square, exacerbates the effect - couple it with an overhanging structure (boom/dipper on the Hydra / Boom on the Rapier) and it tries to hop back and fore, axle to axle
It's a very un-nerving experience the first few times, 'til you learn to either drive through the 'spot' or slow down a little 'til everything settles and go again, ready for it to happen.