I suppose if you keep up the repayments, eventually your score will improve and you would be able to get a new credit card with a better rate. A mate of mine tried to negotiate with Barclaycard and they wouldn't have it. I suppose they take the view that a deal's a deal - and whilst your paying up they are happy to take make profit out of you.
Are you sure your credit score is so bad? You don't say how many repayments you missed, only that it affected two cards. Most people miss a payment from time-to-time and it's not fatal. I missed two on one account. (A dormant account got fraudulently used. I was overseas - didn't see the statements until I got back. Got the money, fees, and interest back, but I had "missed" two payments. I was told that "no negative entries had been made against my credit file". Well, about 18 months when I got the Experian printout I'd noticed that of course these late payments were noted. But in the meantime I'd successfully applied for two new cards.
A friend of mine used to work for a debt counselling place. When people came in with problems they'd write to the credit card provider and usually got interest frozen on the basis the agency was helping them with their debts. I don't know if it gets recorded on your record (as maxsteam says). Afterall, its not a IVA or something "official". Anyway, if you think you are stuck with 26.9% on Barclaycard, it's got to be a good idea. In time, credit ratings self repair. I would just try this route if nobody else comes up with any other idea.