Basically the pre-1958 Wallace.
He refused to join the Dixiecrat walkout at the 1948 convention. As a judge, he required opposing counsel to address J.L. Chestnut as Mr. Chestnut. He was a disciple of Folsom and ran exactly the type of campaign you mentioned.
After losing to John Patterson, he said, "John Patterson out(black)ed me and I'll never be out(black)ed again." Except of course he didn't say black.
I gained some ideas from that (I started the thread so I'm
uncomfortable with this, but here they are):
So make him win in 1958 (Patterson gets an accident or no immediate NAACP endorsement of Wallace, AFAIK it hurt him), so he wins the 1958 Democratic Gubernatorial Primary.
IMO, this could cause a great split within the Alabama Democratic Party, as it would still be filled with racists. Pattersonian Democrats would be wary of his moderate stance on Civil Rights.
It's like the Texas Split in the Democratic Party when John Connally was elected governor, only that the Governor Wallace here is moderate-to-liberal instead.
Because of that, party tensions escalate, and maybe Kennedy visits Alabama instead of Texas on November 22, 1963 so he lives.
But let's go the scenario that JFK does get assassinated. LBJ replaces him afterwards.
ITTL, there's no Stand in the Schoolhouse Door, so Wallace has to gain national prominence in some other way. His racism did it, but he was so opposed by the Democratic Party establishment because of it. Here, he has the favor of the Democatic establishment, but hasn't gained national prominence, just some moderate governor in the Deep South (like Jimmy Carter).
In 1964, Johnson wins in a landslide against Goldwater. The Wallace/Folsom machine manages to swing Alabama to the Democratic column.
In 1968, LBJ bows out due to health reasons, and HHH gets the nomination. He has Southern VP choices: John Connally, Al Gore, Sr., etc. and George Wallace.
HHH may choose Wallace for economics and appeal, and coming from the Deep South, he could swing the South to HHH. Maybe he gets the "national prominence" there.