I don't see a conflict here. Aren't both Border Cock and Malcolm correct? The song obviously has many versions, some with car and some with bar. The both make sense, now that we know what each alludes to.
If Malcolm is correct about the earlier versions showing car, then it seems probable to me that car was most likely the original word but that someone either misheard it or, better yet, saw an opportunity to extend and enrich the bantam cock metaphor and simply changed it to bar. Such is the nature of traditional song.
If this IS what happened, we can say the car version is more historically accurate, both in reference to ballad sheets and to Napoleon's conveyance, but also that the bar version is poetically stronger with the extention of the metaphor. After all, if a bantam cock is an apt image for Napoleon, then a fighting bantam cock is even more apt--a richer image.
Personally, I like the word bar better, now that I know what it refers to. And Malcolm, it does seem to me that Border Cock makes a passable case that somewhere along the way in the transmission of this song, cock fighting people got ahold of it and simply changed it.
At the end of the day, we each will pick the version that appeals to us more. At least now we know a whole lot more about it than anyone in our audiences will probably ever want to hear!
Thanks, everybody, for all the info.