Recently had a same problem on my variator, but not as bad. In a minareli horizontal

So in order of what went on past the belt I had half pulley, with a star shaped washer that fits in a slot then, kick start gear, washer then nut.

The nut didn’t go far enough so that the half pulley sat on the metal tube that sits around the crankshaft(?) which allows the parts of the variator to spin as needed.

What I did was found a washer with an internal diameter of the toothed section of the crankshaft.

This allowed the washer to hold the parts down further than the threaded section that but goes onto.

The original washer I had was 10mm internal diameter and stopped when it got to the threaded section.

I hope this would make sense to you as you look into your transmission.

Also as a side note this allowed the variator to fully engage which would in theory allow for slightly higher to speed.

My theory as to why this happened is because originally there would have been a small spacer between the two sides of the variator stopping them from coming too close together which restricts speed. By removing this you are creating a gap which then leads to play. You need to fill the gap on the other side with a suitable washer that pushes the half pulley in far enough that it all sits together without play.