This may be a bit late, but it becomes FAR easier with the second sword once you get the 3 keycards
Viewing post in The Cog with no Machine comments
I thought the three keycards was part of some required thing, and even after getting the second sword, it makes things harder as much as it makes things easier, as it's now twice as likely to catch a point the "wrong way" and send you moving downwards. I'll keep trying for another 15 minutes, but I may just have to give up on this game again