I'm new at this whole bike thing and I even managed to redish my rear wheel when I upgraded the cassette from a 7 speed to an 8 speed. My wheel was doing the same exact thing. i thought I had a bent frame and it was suggested to me that I redish the wheel. All has been well with the world ever since.

And i would LOVE to know what happens after you mount the rim in the dropout reversed. Sounds like a very logical troubleshooting step.