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You can skip jumping up all the clouds by jumping up towards the top of the screen from different heights.
(Video when ready.)
After acquiring Roc's Cape and jumping up the clouds to the next floor. You can make a precise jump over to the moving platform at the bottom left of the room. Skipping most of the floor and saving roughly 40 seconds.
You do not have to mimic Red Gyorg's eyes to hit all of them, it is possible to hit him with most formations. The .' . and . '. formations seem to work best.
It's possible to hit Red Gyorg's eyes across 2 cycles with the same pair of clones. Video here