Howdy
21252hq's answer is correct. The Uberti redesigned Schofields changed the relationship of the barrel/cylinder gap from the original design. When they changed the length of the cylinder from a 45 Schofield length to a 45 Colt length, the frame was not stretched to allow for the longer cylinder. The spacing between the frame and the barrel no longer allowed for a bushing to deflect fouling away from the cylinder base pin. Essentially the Uberti version places the barrel cylinder gap in the same plane as the spot where the cylinder pin emerges from the cylinder. Without a bushing or gas ring to deflect fouling away from the pin, BP fouling is blasted directly onto the pin. BP fouling blasted directly onto the cylinder base pin of any revolver will quickly bind up the cylinder and jam up the gun.
I shoot a great deal of Black Powder in 45 Colt, 45 Schofield, and 44-40 in Colts, Rugers and Clones. The answer in this situation has nothing to do with the cartridge or the pressure of the cartridge. It has to do with the position of the barrel cylinder gap in relationship to the cylinder base pin. Changing cartridges, or using a lower powered cartirdge will not accomplish anything. Trust me on this, I have been shooting nothing but Black Powder in all my Cowboy guns for years. Without a shield to protect the pin, fouling will be blasted directly onto the base pin and the cylinder will bind. The 1858 Remington New Model Army suffered from the same design deficiency. The cylinder of the Remmie had no raised bushing to deflect fouling away from the base pin.
Cutting the face of the cylinder to widen the gap is not the answer. In fact, open the gap too much and you blast even more fouling onto the pin. It is probably possible to fit a bushing to the cylinder, and cut a relief for it in the frame. The only gunsmith I know of who might be doing this is Bill English of The Smith Shop in Warwick RI. Bill also performs a conversion to make the hand of a Schofield activated by the hammer, not the trigger.
The Smith Shop
The other answer is to use a bullet specifically designed for Black Powder that carries enough Black Powder compatible lube to keep the fouling soft and pliable. If BP fouling can be kept soft, it will not bind as much as it will if allowed to dry and harden normally. Also, you cannot use conventional Smokeless bullet lube with Black Powder. You must use a lube specifically formulated to keep BP fouling soft. Otherwise, you will quickly build up a coating of hard fouling that is difficult to remove.
There is a specific line of pistol bullets that have been recently developed specifically to carry enough lube for rifles and pistols for Black Powder cartridge shooting. It is the Big Lube line of bullets. I used the PRS 250 grain Big Lube bullet in all my 45 Colt loads. There is also a 200 grain version called the J/P 45-200 that works very well with the 45 Schofield cartridge.
Big Lube
P.S. I would NEVER add Smokeless Powder to a Black Powder load. If you want cleaner burning Black Powder loads, choose a better grade of Black Powder. Goex is notoriously dirty burning. It leaves the most fouling behind of any of the commonly available powders. Swiss is the best on the market, but unfortunately it is also the most expensive. Swiss uses a better grade of charcoal and produces less solid particulate matter than Goex. It is preferred by BPCR shooters because it burns so clean. The new entry to the BP market is Shuetzen. Shuetzen is made by the same people who make Swiss, and it uses the same high grade Buckthorn Alder charcoal. It leaves less fouling behind than Goex and will keep any revolver rolling longer simply because there is less fouling blasted onto the cylinder base pin. The good news is Shuetzen costs about the same as Goex, so it is really a no brainer these days to use Shuetzen if you can find it.