He actually could have saved a little time with a little glitch involving the Bird. If you call the bird and you charge your pegasus boots and run towards the bird. He will pick you up and you'll be able to pick your location. HOWEVER, when you land, you'll be running as if the pegasus boots were charged and all that.
That glitch can only be done on the GBA version. The same effect is however used in this run: The Itemdash glitch. Seen at for example 1:17:05. In both GBA and SNES, you have to enter some kind of stairs after activating the glitch, in order to run fast.