I don't see 1948 without a Dixiecrat ticket. A scenario without a progressive ticket would be possible, but the Southern racists strongly opposed Truman's racial policies and he, although I admire this president, wasn't that kind of figure like FDR who hold the party factions together.
Even without an official convention, some southern states would have voted for write-in ticket.
Harry S. Truman (inc.)/Alben Barkley: 388 EV. (52.5%)
Tom Dewey/Earl Warren: 115 EV. (45%)
Unpledged electors (Strom Thurmond): 28 EV. (2%)
The only states Thurmond and Wright carried were states in which the Democratic electors were pledged to Thurmond and Wright; they carried NO states where they were a "third party" slate.
The makings of a shift to the GOP by Southerners was in process in 1948, but Dewey was a liberal Republican, and not the kind of guy establishment Southerners like Harry Byrd would want his state to get in the habit of supporting.