In the post 100% world, if you skip all the missions by jumping the wall to the power up gate and defeat the boss (again), the game thinks you have collected all the gems and completed the area, would that count towards the speed run? Or do you physically have to finish the missions.

If there was a way to skip into the Sorceress re-fight and killing her gave you everything to reach 117% then it would be fine. That sort of thing does not exist, however.

Not quite sure what you mean, do you have any more clarification or maybe a video?