G'Day Sam, I don't see how I can top anything Cal said in regards the rate of flooding, but I think you may find it useful to take a look at the ship's general plans. The icecube tray comparison is a little misleading to describe how the flooding progressed in that water did not just go up one side of the bulkhead and down the other side.
There's the matter of the deck being in the way so once the water had come up, it would first flow forward to fill anything that hadn't been flooded befor moving aft. After that, it would have to find ways to flow back down into the aftermost compartments.
Anyone who has actually served on a ship, particularly a large one, knows that a ship is a veritable rat's warren of passageways, corridors, rooms, vents, wireways and plumbing. While not watertight, any number of non-structural bulkheads would have served to slow down and/or channel floodwaters until it either percolated through or burst through. Corridors (like Scotland Road) would have channeled water along certain routes until it could find it's way down through deck hatches, scuttles, ventilation ducts as well as into any spaces on that particular deck.
I can't speak as to how many watertight sections would have to be filled befor the ship broke up. In this case, it's more a matter of going down by the head as opposed to say capsizing. With the stern coming up out of the water and with it's weight supported by nothing, the bending loads imposed on the structure were simply more then it could survive. I'll leave explaining the math to chaps like Cal Haines who is a far better number cruncher then I'll ever be, but it's really not rocket science. Bend something past the point that it can survive and it breaks
Cordially,
Michael H. Standart