When I spin my freewheel by hand, the whole gear cluster wobbles in and out. It's not loose and there's no play, but all 7 cogs move together in and out as a unit, making gear shifting difficult in practice.
The rear hub is in good shape, in fact. just rebuilt.
Is the issue with the freehub body or with the actual gear cluster? It's one of the Shimano 7-speed cassettes where you can't remove individual cogs except for the outermost cog.