[Lynn Eades]

Hanno, I am not familiar with the set up, but it sounds like you have a spacer and shims between the two Timken taper rollers.
It sounds like you should remove? (or add?) a shim and try again.
You would need to first check that the bearings are in good order. (check the inner races under the rollers).
When checking to find out if any movement (play) is in your king pins or wheel bearings. When you have the wheel off the ground and you are moving the wheel in and out (top and bottom)
If you have someone apply the brakes, and the movement stops, it is the wheel bearings. If it continues, it is the king pin bearings.