Spoke to my real manager, and in his words, "Okay, we'll squash that project." He sounded very happy to hear from me. We don't talk much.
Yesterday the feeling was pride at my own perceived cleverness. Today I could care less who said what, whether it was me or not. The overwhelming feeling is simply sheer joy at being released from a project that should not occur.
Oh, and I took an opportunity to put in a good word for my counterpart on the project to my manager, taking note of a hole in the org chart next to me.