I don't believe I have ever seen an authenticated cylinder pouch, but that means little. Fumbling with a cylinder is always going to be slower then drawing a second loaded handgun.
I've got to agree with the sabre being the weapon of choice for the Cavalry. (Once the war ended though, the Cavalry was used more as Mounted Infantry and the weapon of choice became the rifle, ultimately, the Trapdoor Springfield.)
At some point linen cartridges were also offered but I believe they were intended to be used in long arms. Long ago, I made up paper cartridges to use in a Burnside carbine I hunted with. They worked great with the musket caps.