So the video description says that the "backing track is a blend of the original and MysteriousBronie's version." It figures that the show version's karaoke file has the same tempo and pitch, and can be applied to this song with just tiny corrections. I'll check that out someday.
Update: Audio is in the cloud, along with lyrics, near-correct pitch and not-that-correct sync (edited from the show version file). Finishing up later.
Aaand the song's finished. Needs a cover, though.
I'll look into that eventually. Thanks :P