Gearbox issues

Back to basics.  Primary chain case off.  Make sure the clutch bolts are screwed tight if it's the original type Norton clutch.  It sounds like they are loose.  Possibly because the AMC box has them slackened back a bit to adjust the pressure plate lift.  Unlike the Norton clutch for Doll's Head and Laydown boxes where they are snugged down and the plate is lifted square by the 'mushroom'.
 

All were originally 3 spring clutches whether AMC or older Norton clutches. The only exception were the Sturmey Archer clutches on pre 1931 singles which were either a single large spring or 6 normal springs.
 

As David advised, if you have a Norton clutch then the springs are tightened down fully. Only AMC clutches have the springs backed off to get even lift on the cover plate. 
What year is your machine?

... is that the so-called AMC type has an adjuster in the middle - the original Norton one doesn't and it has the mushroom lifter. The former needs the springs adjusting for even lift; the latter has the bolts tightened right down as the mushroom gives the even lift automatically.

.... and yes, the shock absorber is in the clutch centre.

You will get different views.  90 grade gear oil has similar viscosity to 40 grade engine oil at gearbox temperatures.  A 20/50 (which you might have in the shed for another vehicle) is essentially roughly a 20 grade engine type oil at gearbox temperature (which is lower than engine temperature, so multigrade is not appropriate).
Just make sure you keep it topped up!  You might be lucky but don't expect the same amount of oil to be in it when you take it out after a rest.  
I use the same oil as in the engine, just to keep life simpler.  It has straight cut teeth so high pressure additives designed for hypoid gears ought not to be needed.

When 20/50 and similar multigrade oils became readily available in the late 1960s,  Castrol promoted GTX as a 'one type suits all' product. They even produced diagrams showing that it was suitable for use in the engine, gearbox, forks and primary cases. It probably did not have the refinement of a dedicated EP80 or 90 oil for the gearbox but did save having lots of half opened tins of varying grades lying around the garage.
John Hudson used to swear by it and he rode tens of thousands of miles each year.
As seen below is quite a useful chart.