The connecting shaft itself has " sliding room".
Do you have and good industrial supply places near you?
Can you gat the existing shafts out and with a lathe, do work on them if needed?
Not sure I a replacement female that is not worn out will have better fit either.
Stepping way out of the box...
First locate a sliding coupling, common for farm equipment.
This will be your new shaft.
Determine how to interface, maybe turn existing shafts to nearest standard size or if you have a shaper you can make new females that just fit.
End goal is to no longer use slides on existing interface but to have a telescoping coupling between them.
Use a set screw to seat to shaft, make a mark with screw then drill out a hole to seat it in for locking.
Many options....
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