Apart from Dewey's popularity as governor, keep in mind that Henry Wallace got 14% of the vote in Manhattan. A part of Stevenson's improvements in 1952 would have just been Wallace voters coming home.
Ironic since Stevenson was probably to the right of Truman and I’d think they’d have found him even less appealing. Then again I guess that it being the McCarthy era maybe led to a lot of them reluctantly seeing him as a lesser evil.
Perhaps, but Stevenson didn't have a serious left-wing challenger the way Truman did, so it didn't really matter that he was slightly to Truman's right (and I emphasize slightly - in those days of broad and loose partisan coalitions, Stevenson was not remotely on the right of the Democratic Party)