I think the best description of what happened after the Civil War is that they resumed fighting but by political means. The KKK was a paramilitary group in this sense: their primary targets were black politicians, carpetbaggers, and scalawags. Anyone who voted Republican or supported the party was a target. The South's first pieces of legislation were black codes that essentially reinstated slavery and chained up every freed slave they could.

The Union, in turn, threw out all these laws and their elected officials. They refused to allow high-ranking Confederate officers or land holders to vote or hold office. The South was broken up into occupation zones and they had to rewrite their state constitutions to ban slavery and enfranchise black voters. This basically ensured Republican victories in these states when elections came. The right to vote was a particularly bitter point because most Northern states did not allow black people to vote but forced it on the South.

1874 is when the South began to make significant gains in the House and Senate with Democrats winning seats and Southern states complying with the terms of rejoining the Union. Although in 1876 Hayes was a Republican, the election was contested enough that to make the South comply with the results the North agreed to stop interfering with the South's political process.

The first Jim Crow laws were introduced via constitutional amendment in Mississippi in 1890. After they passed muster, the other Southern states followed suit.

It's a really complicated topic though and each state had different struggles.

Bonus: Mosby of Mosby's raiders thought the Lost Cause was stupid.

Source: Eric Foner's Reconstruction and David Blight's Race and Reunion

I hope you don't mind if I just speak to one part of your hypothesis as it is a subject of unique interest to me.

It's a good thought on Col. Mosby, however he commanded an irregular unit of the Army of Northern Virginia, not a resistance group. His force was not one of questionable legality, but were partisans. As such he was bound by the surrender of General Lee at Appomattox, who was his overall commanding officer. Some of Mosby's men expressed desire to ride further south and attempt to meet up with Confederate units still in the field, but Mosby quashed the idea and sent his men home, suggesting reconciliation instead of a continuation of hostilities.

To clear up any confusion, I believe your use of "paramilitary" and my use of "irregular" is one in the same. In that vein, it is important to properly define what exactly constituted an “irregular” during the Civil War. The term irregular could encompass combatants ranging in scales of legality from the bushwhacking guerrilla to partisan soldier, essentially any action that did not involve the main body of either army. According to Robert Mackey in his book The Uncivil War, partisans were “elite conventional forces given an unconventional role.” These soldiers and their functions were distinctly different from that of the guerrilla, combatants who Mackey characterized as “sets of armed men in times of war, who form no integrant part of the organized army, … and carry on petty war chiefly by raids, extortion, destruction, and massacre …” While Mosby’s men often referred to themselves as guerrillas in their own writings, as did Northern soldiers and press, they were firmly partisan soldiers – legal, uniformed, organized combatants – capable of conducting extraordinary tasks.

Partisans were soldiers, not civilians, and were as such protected by the rules of engagement. They could not legally be executed when captured, and captors were bound to consider them prisoners of war. Guerrillas, on the other hand, were often no more than bands of criminals or brigands. They were civilians, and rarely (if ever) recognized military authority –thus they legally could be executed upon capture. Their aims were usually to plunder or to terrorize and thus served no military objective. Mosby’s men found themselves under direct command of their parent army, but they performed irregular functions such as raiding and reconnaissance.

John S. Mosby enlisted as a private in the Washington Mounted Rifles at war’s outbreak, which was soon incorporated into the 1st regimen of Virginia cavalry, commanded by Colonel J. E. B. Stuart. Acting on Stuart’s orders, Mosby distinguished himself as a capable scout in several actions around Centerville, Virginia in the waning months of 1862, revealing his ability to go among enemy lines and gain information. Stuart most obviously took note of Mosby’s cunning and skill, because he quickly gave Mosby more responsibility.

Mosby himself described the exact moment that he evolved from regular cavalryman to partisan irregular. In Mosby’s War Reminiscences, published two decades after war’s end, Mosby described a raid conducted by Stuart’s command on Christmas day of 1862 leaving from Dumfries, Virginia and ending in Loudoun County, Virginia. As Stuart was leaving Loudoun, Mosby spoke with him: "I went to his room, and asked him to let me stay behind for a few days with a squad of men. I thought I could do something with them. He readily assented. I got nine men … who volunteered to go with me. This was the beginning of my career as a partisan. The work I accomplished in two or three days with this squad induced him to let me have a larger force to try my fortune. … I went and never returned."

Mosby did not receive his first official commission until March 23, 1863, though he had been leading men in his own style of warfare for several months already. He thus organized the 43rd Battalion, Virginia Calvary under the Partisan Ranger Law newly passed by the Confederate Congress. According to this law, Mosby’s orders noted that his battalion would be “placed on a footing with all the troops of the line,” but the Partisan Ranger Law additionally afforded Mosby’s men the right to the law of maritime prize, whereby his troopers were allowed to keep the spoils of war.

These men were no longer regular soldiers, but partisan rangers. Their purpose was to conduct irregular warfare, and they were legally permitted to confiscate anything possessed by the enemy. These actions were intended to both further harm the enemy and to provide incentive for joining a partisan unit.

Thus, the men under Mosby and the actions they performed were perfectly legal under the auspices of war. Their demographic makeup was different than the regular army, as many of Mosby's men were from high society - sons of Virginia wealthy and/or influential. In fact, as John Munson (one of Mosby's key men) put it “his [Mosby's] recruits were some of the very best blood the Confederacy had to offer on the altar of faith.” While as stirring as that quote may sound, these men had direct family ties to Confederate leaders, and respected their surrender.

That is not to say some of the Raiders did not take part in the violence that ensued after the conclusion of the Civil War - they just did not take part under the banner of continued military resistance.