It really sounds like the "bore" needs a skim to enlarge it then use anti seize. Sounds like the rust on it is growing so may be time for a good skim to get back to the original & it probably only needs a few mm gone..
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I was always taught that “copper anti seize grease” was not a grease as such but was to be used as a grease, but only to stop things seizing, such as nuts or for example the screws that hold brake drums in place or other items that are not removed very often.
Yes, as the name suggests it's to prevent threaded things seizing.
Works really well on adjustable top pto links on tractors where grease goes hard, etc.
I know it ain't the ideal thing to use in the case in question.
cheers, DL