I started driving on Minis and the inner joints on those were rubber cruciform types. They were clamped in using U-bolts and if not properly aligned would cause the shaft to run out of true. This had two effects : firstly they would be out of balance, although as they were relatively light weight this didn't cause much of a problem. The other effect was that it cased the wheel rotation to be very slightly uneven which reflected through the steering as a wobble. This was noticeable at low speed more than high. The joints were always troublesome because they got oily, the rubber swelled and they started knocking on the transmission casing.
Modern shafts use the tripod joints with needle roller bearings and don't, as far as I know, suffer from misalignment but as you seem to have eliminated wheels and tyres as the source of the problem I just thought it would be worth checking to see if the shafts are running true or, worst case, bent. The only way I know of is to jack up and turn the wheels whilst looking at the shafts.