G'day Big Seven.
So yours is a plunger with the better early six spring? At rest the basket/chainwheel will wobble a bit, I would say 2-3mm would be max. It will tighten up with the hand lever pulled in. When running it will find it's happy place. Do not over tighten the chain. The three things that wear are the rollers (18 of them), the thrust washer (that the rollers roll on) and the race in the chainwheel (that the rollers roll in). Also make sure the thrust washer abutment ring (two halves) are seated correctly. It wouldn't hurt and cheap to throw a set of rollers in and give it a go.
Cheers