Penny Pringle getting booked into second class passage wasn't an oversight.
Someone at the Secret Intelligence Service knew about the Titanic mission and sabotaged Penny's accommodations. Carlson didn't actually travel trough time....
He actually died because of the blast and the game's events are his afterlife. The events of the game were Carlson's Coma Dream.
Which is sort of similar to how Tanner in Driver: San Francisco played out the events of the game whilst in a coma. Carlson took on the role of his younger self in his dreams, and went on to settle some unfinished business, which would turn out to be crucial for the situation he was in London. The painting was later reproduced.
The painting is a real one that was made by Hitler, who actually made it in 1914 and the painting in the game is mirrored. Perhaps the painting in the game was the original, and after it went down with the ship, he tried to recreate it.