I wept like a baby during the entire sinking part of the movie but not for Rose and Jack, or any of the main characters. It was the ones you said, the band, when they realized they weren't going to survive just started playing again is just such a powerful moment, the Strausses holding each other as they went down gets me every time, Victor Garber's character watching his beautiful ship going down. Hell, I lose it every time I watch that magnificent staircase start to fill with water.
The sinking really was cinematically perfect...until they focused on Rose and Jack and that stupid door. Everything else, though, was stunning and heartbreaking and a master class in film making.
I wish they had given the movie a different focus than the "forbidden" love story but I also don't think it would have been nearly as financially successful if they didn't have the two young, pretty people from different social classes falling in love and one dies tragic love story the general population eat up so I have to suffer through it to watch my beautiful ship. (I'm slightly obsessed with the Titanic, the ship as well as the true story of the sinking).