I don't think Liberal-Conservative is a good scale for measuring Confederate Candidates. According to the Book Look Away, the four main camps seemed to be Nationalist (favoring a stronger central government), Moderates (generally opposed to the power of the Davis government), Fire Eaters, and Reconstructionists. My guesses on that division are below.
Extreme Fire Eater
Robert Rhett
David Atchison
Fire Eater
Robert Barnwell
Mild Fire Eater
Louis Wigfall
James Chestnut
Nationalist
J C Breckenridge
John Reagan
Mild Nationalist
Robert Toombs
Robert E Lee
Extreme Moderate
Joseph Brown
Moderates
Alexander Stephens
Howell Cobb
Robert Hunter
PGT Beauregard
Wiley Harris
Mild Moderate
Joseph Johnston
Mild Reconstructionist
Zebulon Vance
I'm gonna try and turn Fiver's list into political parties as it presents more than enough differences for the formation of Political Parties. Also the more I think on it I feel that the CSA might become a multi-party system instead of a Two Party system.
The Know Nothings: Extreme Fire Eaters
The States Rights Party: Fire Eaters, Mild Fire Eaters
The Confederate Party: Nationalist
The Patriot Party: Mild Nationalist
The Whigs: Moderates, Extreme Moderates
The Southern Democrats: Mild Moderates
The Copperheads: Mild Reconstructionist
All right best I have come up with so far I know that some of the names have been used by turtledove (Confederate and Patriot Parties as well as the Whigs) I tried to name the parties as close to historical background as possible. Names of the two Nationalist Parties kinda name themselves in my opinion. The Know Nothings were an antebellum party that kinda fit into the Extreme fire eaters. The Whigs really were trying to reorganize them selves within the confederacy over the course of the war. while the Mild Moderates became the Southern Democrats and the Reconstructionist I named the copperhead because it just seemed to fit.
you would probably see alliances between two or more parties when it comes to presidential elections