I have the exact same problem on my 74 Cuda and I also have the hotchkis control arm with adjustable strut.

I've removed all the play in my LCA and welded the stiffning plate. I also revert back to the OEM rubber bushing just to see if the poly bushing was the cause.

It is driving me nuts but I think I've found a promising clue. My problem is on the passenger side only and I have noticed that the adjuster screw is not centered inside the LCA when the car have the weight on wheels.

Almost as if my LCA was twisted and I can see some rubbing marks on my fresh poweder coating so I think I will try to find a used set of LCA to test this theory...