This is a cool idea; I actually just grabbed the movie and have been meaning to watch it again.
It might be an interesting spin/alternative to look at another war movie -- heck, any movie -- that has a lot of memorable scenes and acting them out with Joes. It'd add a lot of depth to replacing the characters, figuring out who would work with what line, etc.
Full Metal Jacket, Bridge over the River Kwai, The Great Escape... or, if you wanted something funny,
Dogma or
Office Space could produce some hilarious scenes or dios.
