Effort should of course be the same turning in either direction.
I'll assume you've bled the system, as you said the steering wheel stays straight when running with wheels in the air.
If it changed with the box, that would seem to pinpoint the area of the problem.
As far as being darty, I'd expect that to be an alignment or even a tire problem, if not a rutted road.
If one or more of the bushings has deteriorated, the steering and/or suspension settings are moving as you encounter variances in the road surface, right ?
I've also had that happen with square-shouldered radial or bias-ply tires on rutted road surfaces.