Switched parties. That’s about it
If Edwards were a Republican, he would have won the runoff outright with well over 60% of the vote.
If Edwards switched parties, he'd have finished 3rd in the intial race. Maybe 4th, because he'd be part of a field that would likely have included a prominent black Democrat, or a lesser Democrat.
Buddy Roemer switched parties and lost reelection. He not only lost to Edwin Edwards; he lost to David Duke (as did Republican Clyde Holloway, who was the establishment GOP's choice).
I wasn't discussing a party switch. I was stating what the outcome would have been if Edwards were running on the exact same record, as Governor, but were a Republican, not a Democrat.