EDIT: Better description in the newest post.
Like Sonic's Speed Shoes, which make the music faster while active, but the music continues from the same point, it doesn't start over.
I had a solution for a similar problem where a new instrument overlays the current track, by having both songs (with instrument and without) play at once, and you mute one to switch them. That ensures they'll play at the same point in the song when switching, but since speeding up the song, y'know, changes its speed, that solution can't work.
Is this even possible?