I had similar problems with ex mil 5.56 military brass.
I think you'll need to borrow/buy a swaging tool. RCBS makes them, they press the primer pocket into uniform size.
It will be more practical to put the problem cases aside for now, and wait till you have a large enough amount to bother with.
I have deprimed lots of live primers without a hitch, just take it slowly for a start till you're comfortable doing it quickly.
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