The wheel mounting design leads to some slop in the location of the wheels. In taking apart the mechanism, it appears that the slop comes from the plastic bushings not locating the driveshaft precisely. I'm going to try and replace at least one of the bushing with a larger metal bearing to see if that helps.
I may also print a new housing that locates the shaft inside the bearing and forms the outer third of the universal joint in the driveshaft mechanism. More to come.