The entire structure of the Enterprise in AGT was different, wasn't it? I thought I'd seen it listed as a different Enterprise as well somewhere ( a model kit I thought, but I can't recall).
The one with the C didn't change on the outside other than damage, and the interior was refitted for combat situations.
The one I'm referring to was a 3-Nacel Enterprise I'm sure... I don't recall where though. I easily lose track of episode names, etc.