Accepted REA, but my school won't let me apply to others RD. How can I get out of this?

Hello. First of all, congratulations on your acceptance. I’m sorry to hear that you have changed your mind about fit. It happens!
I definitely disagree with Twoinanddone about turning down the spot. Don’t do that! So risky.
I’m assuming that you may be into H, P, Y, or S, because those are the only schools i heard of that have REA, but of course there could be others that I’m not aware of. If that’s the case, turning it down and then applying elsewhere RD may not work out as the acceptance rates at these schools are so low. It also may not satisfy your high school because it sounds like they want you to be “done”.
I had heard that certain top private schools like to manage their applications this way, and personally I understand how it works out best for the total school population, but I’m not a fan of limiting choice. However, it sounds like you agreed to it. In which case, if you want school permission to defy the rule (and their permission is needed for recommendations and transcript), you need to be very very nice and do your best to make a case for why you think it’s no longer a good fit. You catch more flies with honey, plus a persuasive argument.