There is a consistent way of skipping the Lights-Out sequence on the 3rd Floor: Save the game when the sequence starts, and load it immediately.

Consistent setup for frontloading the final puzzle:

Step 1: Create an invalid savegame fie, for example an empty file

Step 2: Beat the game (you can load from a save near the end)

Step 3: During the ending cutscene, load the invalid game file to go back to the main menu

Step 4: Play the game, the final entering of names will be skipped.