The person that made the video walkthrough jerks the camera around and often changes his actions and repeats actions. I watched the part following installation of the rails. The following actions, to get out of there is senseless. so I opened options and chose teleport to a safe site to get to the intended location.

Does anyone have the proper steps to leave the vertical cart track puzzle?

There is a written walk-through which is better for getting hints/reducing spoilage: fisicx.com/firmament/index.html

Enjoy!

~f