If you'd like to remove the dependencies on getUnusedFilename and the mime mapper stuff, you could do something like this:

var filename = Math.random().toString().substring(2) + '.' + memoryBackedBlob.type.substring(6);

That is: pick a random number, remove the "0." prefix from it, add a dot then add the mime type with the "image/" removed from it.  The chance of getting a filename collision should be vanishingly small.  And for image types, I think stripping the image/ from the type will always yield an acceptable filename extension.