Note there are two 37's in the top drawing. It's a drawing mistake.
The writeup is a bit hard to follow.
Nothing should wobble in there. The lower pulley (below the crank drive pulley) towards the tractor section is the tractor drive pulley. The pulley (14 on the first drawing) moves in and out when the cutch handle is pressed.
It moves out by the force of the clutch and returned by a spring. It should not free wobble.
14 is screwed on by 37 to 16 in the second drawing. An arm (not shown) moved by the clutch handle catches 24 to move 16 in and out. 14 moves with 16.
The movement of 16 brings the drive plate up to the friction disk. It’s doubtful 16 is bent. Possibly your pulley could be bent or bearings so worn they do not hold 16 steady.
I don’t see how you could get a big vibration in there unless 16 is somehow so loose it contacts then goes away from the friction disk at a high rate. But that would engage and disengage the friction disk causing chugging of the wheel drive with rapid stop and go movements.
You could get some weird vibration if the back auger drive bearing was worn and the auger drive shaft able to move around.
There is no torque spec mentioned in the service manual for 37. A good crank should be enough. It just holds the pulley. The force is on the pulley key.
>> I NOTICED TOO THAT THE FRICTION PLATE SUPPORT HAS NO LUBRICATION.
If you are refering to the assembly in the lower drawing it should get lub. The hex shaft can be cleaned with carb fluid and get a film or light oil or grease that won't dry out i.e. no white lithium.