For years my 126 drove me crazy with vibration. I could get new tires, get them perfectly balanced, and it would shake like crazy. I drove the tire guys mad, insisting they replace the tires and doing re-balance.
I replace every part under there, and adjusted the steering box and the wheel bearings numerous times.

Then, after a perfect balance job on new tires, using the vaunted Hunter force machine, I had the same old shake-shake-shake. But, I discovered I could just remove a wheel/tire, and put it back on again, and the vibration changed or totally went away.
The only thing I could deduce was that the wheels were not perfectly hub-centric, even though I could put a dial indicator on the two front ones when the car had the shakes, and get virtually zero (0.010") runout on the wheel rim.

Finally I gave up and ordered new wheels and Goodyear Assurance tires from the Rack. All was smooth! But then I found a cosmetic flaw in a wheel, and had to dismount the tire and replace the wheel. Sure enough, when the new wheel arrived, I had the tire put on it, force-balanced on the Hunter - and it shook. We tried a 2nd balance - it improved a bit but still not perrfect.
I put it on the rear, and all is now good, but I dread the time when rotation comes.

But the comment about tire roundness is probably valid. These new Goodyears are their finest tire, but I can see significant vertical runout on all of them, maybe not 1/8" but enough to easily see when spinning the tire.
I have similar runout on the tires on my other cars, and no shaking at all, ever.

So, I submit that the 126 is the most vibration-sensitive car in the known universe!!

good luck,
DG