If your credit and payment history is as good as you say, then you can call the CC co. about every 6 months or so to do the following:
Remind them of your excellent record, then ask them if they will lower the interest rate on your account.
It works. They would rather keep a good steady payer than to have you take your business elsewhere.
Like this:
"I have had this account with you for ____, and the interest rate is very high. Isn't there something we can do to lower this interest rate, and how far can we lower it? Otherwise, it makes too much sense for me to transfer the balance somewhere else."