Oh, I hadn't noticed that third staircase from E Deck to the open space.
Those three staircases were all connected, so I guess the that third staircase let water in as well.
New scenario:
The starboard front side of the open space was the first side to flood. The water leveled with Titanic's list, most likely also wetting the lowest stairs of the port staircase to C Deck.
The open space continued to flood through the fore staircase from E Deck, staying pretty much even with the water level on E Deck.
I don't know for sure what happened with those aft staircases: or they flooded from the already flooded open space down to E Deck, or they flooded from E Deck into the flooding open space, with the water following the pitch. But I guess the water was already close to the staircases when one of these took place.
But there's still a problem: there was yet another set of staircases for seamen at the front side, separated from the open space by a door.
If those staircases went to E Deck AND if that part of E Deck was already flooded AND if that door wasn't watertight, the flooding might have been accelerated by those staircases too.