Well, here's the solution. I am quite proud of it after discovering it on my own. Remember that before entering this chamber you need:
- four pronged orchestrion which plays "Watch Your Step"
- two pronged orchestrion which plays "Traveling Music"
All of them are obtainable from the Chanters Hall (first pyramid). Use the Gold Ring on the hole. Stamblyr will give you "Watch your Step", have La Forge use the Device on the Instrument. Stamblyr will give you "Traveling Music". Obviously to get Gold Ring and the Device (and the Staff by the way), you needed a Thermacode Key used on the Vault, but you would likely already know it if you made this far.
Hopefully this video will serve as a good solution to hardest puzzle in the whole game.