OK, let's think about this:
The only way that a steering head bearing will cause, or more accurately prevent, wobble is if the preload on the bearing is such that it provides mechanical dampening to the oscillating forces that are always present. Kind'a like keeping your hands on the handlebars will.
In other words, the bearings can not be the root cause of the wobbles, however they can contribute to wobble occurring by being too loose.
The root cause has to be something that is actually moving, so it is most likely caused by some part of the rotating mass of the wheel(s).
Since it is impossible to achieve 100% perfect balance on wheels, and since tires will always have some degree of imperfection, having some (small) amount of dampening in the steering head bearings would help eliminate oscillation.
If all of the front wheel variables have been checked and rechecked, then adding preload to the steering bearing may kill the wobbles. The reason a roller bearing would also work is it has more contact area, therefore more friction and more dampening for the same amount preload torque. Plus they can withstand higher preload (for even more dampening) than ball bearings, without distorting the races.
At some point too much preload of the steering bearings will result in handling issues since it will require too much effort to turn the bars to initiate steering. And, especially with balls, may cause premature wear and dimpling of the bearing races which results in notchy (varying) resistance to steering input.
So, both the "tires/wheels" group and the "steering head bearing" group may both be right here.