All 3 gramophones have been in the same place every time for me. Anyone else experience this?
I found a couple issues in the "Take me to the door" section: Right as Valve 3 comes into view, you have to go onto the falling platform, but if you walk towards the valve before it falls you'll end up walking in the air. Valve 3 can be collected from up there, but a bar stops your forward progress and you're bound to always being directly above the path. Walk back to where the platform was and you'll warp down to where you should be.
Additionally, a few frames can be saved when you press the button for the door to make it rise. The actor for the door just spawns where it should be, regardless of how far up the door graphic is, so you can hit the button and enter the door before it rises all the way, saving almost 1/3 of a second.
You can get both achievements at once if you wait until you'd normally get Peek-a-TWO and look through the hole. You'll get Peek-a-boo, then wait like two extra seconds and you'll also get Peek-a-TWO. This saves about 2 seconds because you don't have to go to that room twice.