If the 88 is like the 95 and up...
There shouldn't be much play with the clutch inner cover on. If it has play, it sounds like that cover is not supporting the shaft. I don't remember what kind of bearing is in there... but it sounds like it is shot.
For the engagement mechanism, there can be a few issues. That spring that pushes the gear faces together can have lost it's spring.
The gear ratchet faces can have raised metal ramps. The gears are like metal ramps with steps, so they slide when rotating one way but engage when rotating the other. When they ride up the ramp they can raise a metal lip at the top, which keeps the steps from fully engaging when you try and spin it the other direction. So if you pop them apart, put the engagement faces of each side on sand paper on a flat surface, you can polish them back flush again. You will see when it is all flat again, as the sandpaper polishes the surface. This alone makes a huge difference.
Finally, there is an index mark in the shaft and the lever arm that engages in the case... if you don't line them up, it appears to work OK, but the kickstart lever return spring doesn't have the right leverage, and the whole arm can be floppy.