Ha ha, now we're talking!
I think it is definitely Lordran, thousands of years later. The Cathedral area etc is likely to be Anor Londo all right, and the passage of time might explain why the battery on Dragonslayer's spear died
There is also an NPC (I forget who) who strongly hints that this is the case.
I dunno about the rest of your theory though - if Anor Londo, the highest point, was submerged, then all the rest must be below that (barring any huge convulsions in the land). I'm up under that aqueduct at the moment myself, so I must have a proper look around.
DS2 may feel like a proper world but I think DS1 was better. Brad (again) claims that the world in 1 felt too compact and crowded, but the way I look at it is that that was a vertical slice of a small part of the world, not the whole thing. The world itself extended outwards on all sides, and was chock-full of all those nasty things too.