×So the main gimmick of this room is that during the replay the time clone is offset by two tiles to the left. My plan:

0. Wait a bit
1. During the first pass I push the mirror to (19,19)
2. Kill right eye and move to the left but don't kill the left eye
3. Wake left eye
4. Go down through the right door and kill the mud mother
5. Go up, kill the eye
6. Move mirror to (18,19) ???
7. Go up and pretend to wake the right eye (which doesn't exist anymore in this timeline)
8. Go down again through the right door
9. Go through the green door and end recording
10. Now the main timeline player goes down and activates the token, so when the recording goes left from the tunnel, it's shifted two tiles to the left
11. The recording now pushes the mirror to (18,19)
12. Kills the _left_ eye
13. Goes through the motions to go down via the left door
14. Pushes mirror to (19,19) ???????????
15. Wakes up right eye, guide it onto the plate
16. Goes down, finally kills the mud mother
17. Kills eye, goes through green door

But I have trouble with step 14, because to move it from (18,19) I must push it horizontally, and that effectively synchronizes the mirror between the two timelines.

×I had to go down just once, and didn't have to touch the mirror after the initial setup.