1. OP was the beneficiary of a discounted ticket which had rules. He broke the rules. As a matter of contract, he is out the money. Period.

2. The better way to handle this, having mishandled it in the first place, is to write a short and to the point email (better, use the web form on aa.com), cutting out all of the snark, asking that AA issue him a voucher for the value of the original ticket.

The key here is that AA is not obligated to do anything and probably will not do anything. But, making demands as opposed to asks and focusing in on the key issue will increase OP's chances.

OP's one shot here is that had he called in ahead, he could have used the weather waiver to allow his new routing. But, that's all dependent on being clear and not getting into name calling.