I think I'm closing on the end of the game, although I'm not sure, but there's a time puzzle in one of the throne rooms after you ride the third elevator down. There's not enough time to reach it when the doors close, and constant swarm of Echoes makes everything increasingly difficult. I'm not sure if this section of the game is broken, or if I'm missing some part of solution.

Tried my best for half an hour, but I just can't figure it out.

Got it figured out, for anyone wondering, you're supposed to wait until one of echoes copies you sitting on the throne.
Should have thought about it myself, but asked the devs instead (kind of a dick move, but whatever).

I watched a twitch player run/dash from the throne to the doors, unless this is a different puzzle.