While this isn't my flair, I know enough to answer this.

Your hypothesis is basically correct in that the Confederate States of America, while it existed, was more or less a one-party state. However, there were certainly factions that did not approach formal party status and it's helpful to examine them. But first, lets talk about the people who made up Confederate government. Remember that Confederate politicians were once politically active in the United States and indeed one of the primary Confederate grievances / reasons for secession was the Congressional absence of the Senators and Representatives from Southern States. This idea as an argument of course overlooks that they were voluntarily absent as an act of protest.

During it's existence, the Confederate Congress consisted of 135 seats: 26 for the Senate and 109 for the House of Representatives. The Confederate Constitution was almost a carbon copy of the US Constitution with a few notable exceptions such as the enshrinement of slavery as a permanent, inviolable institution and a different interpretation of what was meant by 'states rights'. The Confederate Constitution created the permanent Congress in March of 1861, but the Confederacy was functioning in February 1861 under a Provisional Government at Montgomery, AL for the purposes of drafting the Constitution. Then, the official capital was established at Richmond. The Provisional Government itself was predated by a convention of interested Southerners that met since John Brown's raid in 1859. The actual conventions on secession occurred only on a state level.

Virtually all of the Southerners that would make up the traitor government were former Democrats, and Democratic ideals dominated Confederate ideology. Just as the GOP of today is certainly not the Republican Party that elected Lincoln, the Democratic Party was also different. Southern Democrats did unanimously reject the second point of the 1860 Party Platform. However, other ideas in this platform remained popular in the South. Industrialization of the South after the war (to which the entire Confederate economy was devoted at the time), without abrogating the quintessential agricultural lifestyle, was debated. Expansionism was very popular and the CSA had plans to expand West and South both during and after the war. Both Democrats in the USA and CSA wanted to acquire Cuba. The CSA also had claims to much of the Southwest and intended to invade Mexico had they won the war.

Prior to the war, there was an organisation called Knights of the Golden Circle founded in 1854 that was pro-slavery, Southern nationalist, and conspired to create a country out of the slaveholding states and territories, Mexico, Central America, and much of the Caribbean. This organisation remained influential during the War but there is no credible evidence that it survived the war.

Lastly, two broad camps of thought existed among Confederate citizens. There was no real middle class, partly due to slavery's existence itself. When an employer could obtain free, forced labor at a negotiable price, this forced wages to remain low for white workers. This created a very broad class divide in the South, with the majority of people (including some slaveholders who only "owned" a handful of persons) living in poverty and literally living season-to-season through subsistence farming and some small amounts of cash crops (notably cotton) vs a very small aristocracy that owned large plantations, grew cash crops exclusively, and had a very large force of slaves as well as other white Southerners in their employ. During the war, Confederates could hire a substitute to fight in their stead. This was also the case in the United States. This proved to be extremely unpopular to Southerners subjected to conscription (who would have thought!?) and it was abolished in late December 1863. Additionally, if a person owned a sufficient number of slaves, they were also exempt from the draft. This was equally as unpopular and helped to divide Southerners into pro-war, aristocratic factions and working class Southerners who more and more turned against the war. When the Union naval blockade of the South succeeded in strangling their economy and caused resource shortages, the Confederate government began confiscating goods from already-poor Southerners, further cementing their feelings that they were simply "poor men fighting a rich man's war".