Found an interesting glitch.if you press the select button several times in the third level before the race, then the race is skipped completely, but you will have to beat the boss twice in the toilet.I'm playing on an emulator (FCEUX) and can't be sure that it will work on a console as well.The video attached

I just tried that, and it works just like you said. I have done that before, but didn't know how I did it lol

I'm not sure if this will shorten the time on Stage 3 or not, but I'll eventually give it a shot.