violent jerk

What engine oil are you using?? A lot of shifting issues can be resolved with the proper engine oil. You need to use a motor oil with a JASSO MA designation, otherwise you'll be plagued with shifting problems

36000 miles is early for chain replacement . Usually 80,000 - 100,000 miles would be more likely.

And if you ask 15 motorcycle riders what engine oil they use, you'll get 15 different answers.
Interesting, the Service Manual says just an SE grade  SAE (multigrade)  JASO MA is a specific grade for motor oils used in engines with a common sump with a standard transmission with a wet clutch.

Maybe something simple like final drive damper? Number 8?

I was hoping it would be the rubber damper but it's unfortunately further up the drive shaft in to the engine.

I had been using Motul 10 40w semi synthetic with some zinc additive. But I've now switched to Westway lubricants 15 40 semi that says it has a good level of zddp. It says it has Jaso MA/MA2 and Jaso 903;2016 .

Strangely I don't have any actual shifting problems with the gearbox itself. I'm always amazed at how precise and solid the shifting is on this bike. It's just when you get back on the throttle that the slack appears in the drive line.
It's a 1979 A1 but has the large sump...if that makes any difference?

Many times I have had transmission problems in agricultural machinery, the first thing that fails or breaks is usually the crosshead bearings on the transmission bars.
Try disassembling your cardan to see how the needle bearings are before disassembling the engine case.

Thanks KawaBCN, I examined the cardan and it seems to operate very smoothly with very little slack. But with the cardan removed I rocked the driveshaft back and fourth, there is a lot of slack / play, on the engine side, but the universal joints are good.

I'm sorry I don't have a better photo.

Where the red arrows point are two bearings that may have worn out, causing the pinion to move, with the green arrow causing clearance between pieces.

You can remove the oil pan and use an endoscopic camera to see a possible failure before disassembling the engine.