Your "thought of adding counter weight to the sub chassis" is a good idea, and Oracle used it, just to name one. It will achieve balance, but the drawback is that your subchassis will ride lower due to the increased weight (and be stiffer). This could make the platter rub against the top of the plinth, but can probably adjusted. Worth trying.
Also, your local hardware store may have a wide selection of springs — mine does — including the tapering ones used in TTs (they curtail side-to-side instability). I've often found the right spring there, without guesswork; they cost almost nothing, and no waiting for it to arrive in the mail. I just take the dubious spring in with me, find a couple the same size but slightly stiffer, and it usually solves the problem. It doesn't have to have the Linn or Thorens name on it — they're all just springs.