G'day Andy,
I've never owned a dishwasher (wife works fine) so can't comment on it's use for cases.
Make sure the other bushes (cam & idler) don't fall out as well. I put a bolt & washers through just finger tight to keep in place.
When done and just before the return of the other half, cook a leg of lamb or similar to disguise the smell of cooked engine parts.

Cheers