I keep breaking things XD. I did end up going back and solving the puzzle in the correct order but I figured it'd be worth warning you about this glitch.
(Manor house puzzle spoilers)
Okay so apparently if you are in mini ghost form, it is possible to fly through the window in the Cthulhu room BEFORE actually opening the window in the Cthulhu room? I was zooming around exploring every room as a little ghost to see if I could find any crannies or holes to fly through, plus it made it easier to find hint coins. I flew at the spot on the wall and suddenly found myself in another room, with the last hand I needed! Unfortunately I couldn't figure out how to get back out again, with or without the hand. I solved the optional painting puzzle on the wall, which put me in a meta frame of mind, so I decided to drop the hand on the floor, log out, and see if the hand showed up in the lost items chest. Which it did!
I put all the hands on the altar (apparently... accidentally in the correct order first try, which was a whole 'nother thing). I'm not sure if the wall opened at that moment, I heard the puzzle solved ding sound but honestly didn't expect anything to happen, I hadn't been TRYING to solve it yet, so I wasn't looking super close. I went back to the lobby and got a hint telling me what to do next and it told me to go to the pyramid room and that was how I realized I broke the sequence of events. ^^;;;;
(...And then got another hint to find out what to do after I finished solving the pyramid room properly and it told me that it had nothing left to tell me and THAT was when I realized I solved the hand altar puzzle completely by chance. When I went downstairs I saw the tunnel; dunno if that was open before or if it didn't unlock until the pyramid room was correctly solved)