[engineer]
to the OP's question about tire design influencing tramlining, there is a definite relationship. i'd say the primary contributor is tire stiffness (both the sidewall and across the tread) and the secondary contributor is tread design.
imagine a tire that is infinitely stiff, ie it does not deflect under load. for this tire, the contact patch is determined by the highest point of the road surface contacting the tire. on perfectly flat ground, the entire tread width will be on the ground and the center of the contact patch will be at the center of the tire width. but as this tire encounters a rut in the road, the instantaneous contact patch is at whichever edge of the tire is contacting the side of the rut, and the car will pull to that side.
the driver's natural reaction is to steer away from the pull, ie if it pulls left s/he steers right.
the problem is exacerbated by wider tires, because both sidewalls are closer to the edges of the rut. closer to the edges means less time between when the rut-induced steering pull changes directions.
now there's no such thing as an infinitely stiff tire, so there will always be some deflection of the tire over the irregularities of the road surface, and the contact patch migration (movement) will be less severe than the imaginary example above.
[/engineer]
if you're gonna be a bear.... be a grizzly bear!