A833 Transmission
it has serious play where the input shaft connects to the output shaft ?. I suspect there is a bearing located there. The tiny teeth (pre 4th gear) are damaged on the input shaft.
Some play at the input, by pusking it sideways ... is normal. The ball bearing that supports it has a tiny bit of axial play
that amplifies out to serious sideways motion, at the end of the input shaft.
Damaged "splines" on the front end of the output shaft arev no big deal.
The clutch teeth on the gears themselves are easy to repair, also no big deal.
The pilot on the front of the M/S can also be repaired
About the only parts in that trans that need to be periodically changed are the brass synchronizer rings, and occasionally, the cluster-pin. And bearings of course. But if you start grinding gears, or have to hold it in a gear because it likes to jump out, well then, before long, yur looking at forks and sliders
BTW
I've never heard an A833 "thumping like a disco" so that will be interesting to see what caused it. I'd be more inclined to think that was in the clutch. But you said;
There is no doubt now.. where the noise is coming from.
so I guess we'll see.
BTW-2
I hated pulling the trans out on the floor when I was 17,
and 50 years later, I know I would still hate it,lol.