Recently I re-played the 2 episodes (and yet again the game surprised me with new opportunities) and noticed another hint right at the start of the game. Emily says you have already met in London four years ago in the prime minister's office, but Louis doesn't recall it at all. When you meet Sarah in the dungeon, she asks, who you are. From the start of the game there were many Amber series easter eggs, and I think, that there is at least one copy of the protagonist somewhere. Maybe Hillsborough twins aren't even sisters, but copies from different Amber reflections. Maybe the servants wear masks, because they all look alike and it's actually the same person.
I actually find your theory quite interesting. I did find it strange that Louis didn't recall Emily at all... So who knows? Another possibility could be that Louis has the power to possess other people, but sometimes doesn't realize it...hence why his mother asks who he is.
As for the servants, they really intrigue me!!! They do actually all sound the same. Döpplegangers? Robots? Supernatural creatures? Personally I lean toward the robot/steampunk/science rocket explanation. The servants are robots/clones and thus all look the same.