Here are the divergences. I think these are somewhat plausible.
1) The Dixiecrats max out at 127 votes.
2) Dewey wins California and its 25 electoral votes.
266 are needed to win.
This leaves the following:
Truman has 161 EVs. Dewey has 214. Dixies have 127.
The vote heads to the House.
In the actual election, Truman won 28 states.
However, in my TL, that becomes 20. The Dixies now have 11 states. Dewey now has 27. And before the House votes, there is of course jockeying. And Strom and the other Dixiecrats now have a lot of power. For Truman to reign victorious, he's going to need them to flip. And that comes at a price.
So, what is that price and how does that shape the next few years?