When there is a written contract that clearly states the terms (and may even expressly state that any amendments must be in writing), you really have little to stand on. Had you wanted another agreement, it should have been included in the written agreement and you should not have signed a contract that you knew did not include the terms you believed you agreed on.
Here in Ohio you might be able to get out of it under our law on Prepaid Entertainment Contracts, but with a quick look, I don't see anything like that in Georgia. Having said that, the internet is a very powerful tool. One thing you can promise the owner is that if he doesn't help you out and do what he agreed that you will tell everyone that you know, and more when you start a blog named "JimsMartialArtsisAwful".
Now, be careful, be able to prove what you say on the internet, and to your friends, as the owner could sue you for slander for maligning his company and calling him a liar. In the past, however, I have found people who have successfully used such threats. You could also tell him that you are going to report him to the Better Business Bureau or Angie's List.
Keep in mind that I am not a Georgia lawyer. Before you start a blog badmouthing him, I suggest that you discuss this with a local attorney who would practice in internet law. Check Avvo, there are lots of listings.
The agreement will most likely be upheld according to the written contract that you signed. It is difficult to determine whether the agreement is valid or invalid without reviewing the terms of the written agreement. You should consult an attorney to review this agreement to help you better understand your rights.