I LOL'ed (ugh, I am that guy that used 'LOL'ed'....) at the idea of drain cleaner, but it might actually work. Not sure if you could get that flavor out. Another idea is some muratic acid from a pool supply store. That is just watered down hydrochloric acid without all the other stuff in drain cleaner that might give off scents and/or flavors. A gallon of the stuff is usually a couple of bucks, just ask for their shock acid. Obviously which ever way you go, make sure and rinse the Hades out of it once you get all the juicy bits out.
The way I see it, if whatever is eating the mice can live through acid and a heavy bleach treatment, you are probably already doomed. The biggest concern is smells and flavors, and you should be able to clean up glass pretty easy. Buy a cheap carboy cleaner brush that you don't mind throwing away and use it to clean the bottom.
BTW, if the carboy is plastic, disregard everything above and just burn it.