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lately I've had great success by just calling CS and asking them to reduce my APR. Done by all I've asked except USAA. Still a couple left to do.
If it is not on a Chase account (Chase does not discuss APR) then you can call in and ask for an APR reduction and see how far you get. As for the increase most cards have increased by 0.25% due to the fed increase mentioned above. Good luck!
Please let us know what happens if you call.