Weird... Well, if you've checked all the connections and they look sound, then I think you got a bad ESC and/or motor...(again?) Are the settings on the new ESC the same as before? High timing/start power would cause this with in-runner motors. Maybe try re-updating the firmware incase there was a glitch somehow.
Sorry to sound like a broken record. If the car coasts smoothly while off power then I don't think it's a drivetrain issue, unless, like you suggested, there is some strange on-power flexing going on.
Could you post a couple pics of the setup? It might help us help you.
