Howdy
You have unfortunately discovered the biggest design defect in the 1858 Remington revolver. The lack of a cylinder bushing on the front face of the cylinder, and the consequent poor performance of the revolver in avoiding cylinder binding.
Here is a photo of the barrel/cylinder gap area of one of my Remmies. The cylinder is a cartridge conversion cylinder, but that does not matter, the concept is the same. Notice how the front face of the cylinder butts directly against the frame. Notice how the barrel/cylinder gap is in the same plane as the location where the cylinder pin emerges from the cylinder. What this means is that every time the gun fires, fouling is blasted out of the b/c gap and it gets deposited directly onto the cylinder pin. As you keep shooting, the fouling works its way down inside the cylinder and causes the cylinder to bind.
Here is the same area on a Colt Single Action Army. Notice how the barrel extends through the frame and the front face of the cylinder is set back from the frame. What you cannot see very well in this photo is the arrangement of the cylinder bushing.
This photo of the barrel/cylinder gap area of a Ruger Vaquero clearly shows the cylinder bushing extending forward from the front face of the cylinder and contacting the frame. Above it the barrel extends back from the frame and the barrel/cylinder gap has been offset horizontally from the place the cylinder pin emerges from the cylinder bushing.
This photo shows the front of an Uberti Cattleman cylinder, a Ruger Vaquero, and a Colt SAA. Notice each one has some version of a raised bushing.
This photo shows the flat faces of the front of Remington cylinders. There is no bushing.
What all this means is it is a losing battle trying to keep the Remington from binding. Yes, you can use the cleanest burning powder you can find, but the Remington design is simply not well thought out for firing multiple cylinder fulls of Black Powder. Remington corrected this when the 1875 cartridge revolver came out and they included a bushing on the front of the cylinder similar to the Colt.
My experience with Remingtons is shooting Black Powder cartridges with huge amounts of Black Powder bullet lube on the bullets and the cylinders still bind up. A wad is not going to help very much.
The simplest solution has already been given. Remove the cylinder after shooting it empty, wipe down the front of the cylinder and wipe down the cylinder pin. Coating the cylinder pin with a good Black Powder bullet lube such as Bore Butter will help a bit, but that cannot take the place of a good cylinder bushing.
One other thing you can try is to cut some grooves around the cylinder pin to hold extra lube. In this photo you can see the grooves I cut in the cylinder pin by chucking it in my drill press and spinning it against a narrow file. This simulates the helical grooves that are cut around the arbor of a Colt style C&B revolver. The grooves served to hold lubricant and make clearance for fouling to build up in. That is part of the reason why a Colt pattern C&B revolver does not bind up as badly as a Remmie does. The other reason is the arbor of the Colt is larger in diameter, which means the fouling will build up over a greater area.
Bottom line is, unless you can find a gunsmith who knows how to install a bushing onto the cylinder of a Remmie, you will always be fighting binding. The easiest thing to do is to simply take the cylinder out after every five shots and wipe down the cylinder face and pin with a damp cloth.
cos I ran out of Wonderlube. Sliding the pin partway out and adding a couple more drops while reloading seems to keep things moving. 
