How could I cancel a bait and switch verbal agreement contract?

Recently I was contacted by phone by the American Publisher's service LLC. They said I had won a $1000 gift certificate and they wanted to ship it out to me. Then they said gave me a magazine subscription offer and said that when I received the gift certificate package that I needed to sign the package and send it back and that would release the certificate and start the subscription. They said they needed my credit card number not to charge at this time but to verify that it was valid for use upon receipt of the signed certificate package. At this point I became very skeptical and told them I think I will pass and they assured me that my card would not be charged until confirmation of the contract. I figured when I got the gift certificate package I could do some research on the company and make a decision on what I wanted to do then. They switched me through several representatives and at one point recorded the conversation and I didn't realize that the conversation they recorded did not mention the deal starting upon me signing the certificate package and returning it to them. Two days later I received the gift certificate package checked my credit card saw that they had charged my account, and checked online and saw that this company was a verbal contract bait and switch scam. My question is what my options for canceling this deal are. Of course I called the company and told them how I interpreted how this worked but they stated that they had me on recording and that return of the signed certificate was not the contract sealer but that during the conversation I agreed to this magazine contract and I'm legally bound.