Dashing off the ledge is 7 frames faster than an optimal quickhop.

When going to either of the side stairs, holding up after leaping off the ledge will ensure that your dash movement stays horizontally grid-aligned, giving you a (frame-perfect) chance for the second dash to be perfectly aligned with the door. Holding left or right after the leap will most likely cause you to be misaligned.

Being grid-aligned will make slightly faster times possible, but it does reduce the frame window for dashing into the door without bonking -- the window is 3 frames when aligned, and 4 frames when misaligned by any amount.

Without boots, it's fastest to leap off the ledge by holding diagonally up+left / up+right when going to the side stairs.

Hookshotting to the torch can save up to 20 frames, depending on movement. Hookshotting to the left edge of the torch is ideal, as it will reduce the time spent maneuvering around the torch.

The lowest y-coordinate at which Link can successfully hookshot is 0112. If you simply hold up+left or up+right out of the door and after leaping off the ledge, there is only a two-frame window where the hookshot will connect with the torch, so it's recommended that you err towards walking further north than this (usually via a small amount of airpumping).

Dashing up the stairs to the third floor is slower than walking.