I would definitely allow for at least horizontal mvmt during jumps, it really is painful to play because of human error, I was only able to beat it after a lot of time and a number of attempts I'm not happy to share X'D
If the movement is based on projectile motion, that should be made more obvious. Being able to hold jump and see some of the parabola that the egg would take would help tremendously in letting people know that this isn't a platformer but a puzzle game based on a certain concept.