Chris, Welcome to the Forum.
The design of the clutch means that the chainwheel will wobble, simply because of the narrow track of the rollers, and the need for a running clearance between the front face of the thrust washer and the back of the chainwheel. If it's any consolation, they all do that, and seem to survive with no problems. The Plunger 6 Spring Clutch is considered to be one of the better designs, before BSA cheapened it for the S/A models, then revamped it at the latter end of production. From an engineering point of view, lateral support is minimal, so the basket rocks.
A few things to check.
With the clutch centre removed, pull off the thrust washer. This should reveal two hardened semi circular abutments, which form a support ring for the thrust washer. They sit in a shallow circular groove in the gearbox mainshaft. On my bike they were missing, the thrust washer running on the heads of the rivets holding the oilseal carrier.
Reassemble the thrust washer and abutment ring halves, trick is to stick them in place with a dab of grease, once the thrust washer is replaced and seated, they can't escape. Add the clutch centre, tighten down with the nut. This assembly should end up nice and solid. Then try a selection of rollers in the gap between the thrust washer and the clutch centre. They should fit without binding, the important dimension is the 1/4" diameter, the overall length of the roller is not so important, as long as it does not exceed the size of the gap and bind. The originals are 1/4 x 1/4" and there are 18 of them. Part number is 26-650.
If all seems in order, try the clutch centre and rollers assembled into the chainwheel. Any slop here is due to age and wear. The usual cure is new parts, even then the improvement will be marginal and most clutches will give satisfactory service with plenty of rock and slop. Change the rollers as a cheap improvement, assemble them with grease. Even with close fitting rollers there will still be rock,and grinding material accurately from the rear face of the clutch centre to narrow the gap is possible but carries risks of causing more problems
One plain clutch plate is slightly thicker than the rest and this goes into the basket first. Clutch is designed to be run dry, primary oil level is critical, plenty on this elsewhere in the Forum.
Tell us how you came to be the owner of a very early machine, head over to the introduction section.
Swarfy.