Is there a reason not to use a lot more characters? If your application's name is MustacheMingle, call the file foo.mustachemingle instead of foo.mumi?
This will decrease the probability of collision to almost zero. I am unaware of any operating systems that don't allow it, and it will be 100% clear to the user which application the file belongs to.
It will be less aesthetically pleasing than a shorter extension, but that's probably mainly a matter of habit. We're just not used to longer file name extensions.
Any reason why this is a bad idea?