See video for demonstrations.

Level 5, combining double jump with flame jump is human viable and probably possible to add to runs. Copy of TAS strategy

Level 8, bonking your head on the ceiling after a double jump may (Or may not?) be faster than jumping to the left. Requires further testing.

Level 13: Faster than TAS strategy by approx 660 ms

Level 14: Human viable version of TAS strategy

When you press jump within 100 milliseconds (approx) of leaving the ground, you can still jump. This can extend the jump, most notably allowing a skip in level 5.

There's a possibility of a small time save in level 4 (Probably not worth actually doing even if it is a time save though).I thought I'd throw this out here to see what people would come up with.