Hey, thanks for bothering to play again, great to hear you loved the art and voices. If you can be bothered, to get back up to the first lever and door, when time is slowed, you can jump on cogs with no problems. That should have been said in the popup when you got the ability.
Unfortunately for us, this game has a lot of content, but because everything's a little confusing, not a lot of people see it.
You've caused us great joy finding the headbang by the way.