So this is a list of when each event occur that are required for the story to continue in story order.

Sixpence

• 1:30 Sixpence leaves room with "Blank"
• 1:50 2 of Diamonds leaves room
• 2:30 2 of Diamonds enters Gun room

Clay and Trinity

• 10:25 Clay drinks his last drink

Willow

• 1:30 Door password 5 of spades
• 3:55 Door password Trinity spider room
• 4:30 Door password 4 of hearts
• 7:15 Door password Ace of spades
• 7:10 Willow dies and Can enter room
• 2:40 Willow picture door
• 4:20 Willow brainwash cut off point

Belle

• 1:50 Pause in the music
• 2:30 7 of Clubs leaves the room
• 2:40 7 of Clubs enters the storeroom

Red and Grey

• 2:40 Red leaves the Lighter room
• 4:50 Ghost leaves room
• 8:35 Red Pulls lever

Aurum and Thanos

• 1:55 Ghost says password
• 2:10 3 of Hearts places arm in dumbwaiter
• 3:05 Aurum leaves roulette room to drink
• 7:40 Aurum leaves last roulette handle

Lucus

• 1:50 Lucus leaves his room for the second time

Hope this is some how useful if any of those are wrong feel free to let me know. Or if there are any other timings you'd like me to record just comment!