Wheel wobble around 60mph - but not wheel balancing

On the assumption it's not happening under braking and the different wheels have also meant different tyres, I'd be looking at suspension components such as ball joints and strut bolts (if, for example, you've disturbed the suspension for any reason). Double check anything you might have disturbed, you might find there's just a loose bolt somewhere that needs nipping up.

Check for play in the driveshafts.

Had that for years in the herald and everything was replaced (because I broke them...). Engine, gearbox's, propershafts, everything.

Turned out the suspension turrets were loose. I'd never had a reason to check them or get access to their bolts. When taking (yet another) engine out I noticed a crack line in some dirt so investigated. They never showed up in MOT's numbering double figures either.

I had similar on my polo, about 60mph it would come come and go. While doing something totally unrelated under the car I noticed that one of the cv boots had become detached and lost it's grease. I repacked it and clamped it back on and the wobble has totally disappeared.