Raise the Titan
Seems like if a remake were in the works, both the historical purists and those liking the novel could both be satisfied by making the raising of the ship "Titan" from Morgan Robertson's prophetic book "Futility: the Wreck of the Titan" published in 1898.
Although completely unrelated to real events, the Titan collides with an iceberg on her maiden voyage and although the bridgework collapses onto the ice, the entire ship slides off and slips beneath the waves.
There's your start for a one-piece ship and you get the same title minus the "ic"
As many have stated on here, John Barry's magnificent score was wasted on this film and should be "raised" for another sailing.
If Irwin Allen were still alive he'd buy the rights to it and use it for a new "Voyage to the Bottom of the Sea" which ironically is what the Titanic took...
"If atomic testing makes ants twice as big as elephants, small doses might make them the size of dogs. Stake a few of those out in the yard, and the kids wouldn't cut across my lawn" -- James Lileks