Well .... There are two schools of thought. One is to load to the same specs as the original loading. Two is load to the most comfortable load to actually shoot on a regular bases. I'm a certified recoil wimp. However, I do think loading to original specs is a good idea. Just ONCE at least. Then it becomes time to consider loads that are actually comfortable to soot on a regular basis.
FIRST CAVEAT: Your Uberti Schofield will not shoot well with Black Powder. When Uberti extended the cylinder length to accommodate the 45 Colt, they eliminated a very important Gas Ring. The gun will foul out rather rapidly. Some guns will not even run for a full cylinder. So your choices will be that Heathen Fad Smokeless stuff.
SECOND CAVEAT: Your gun powder isn't running or burning dirty. Your gun is. Uberti famously provides generous chambers. VERY GENEROUS chambers. Big hurky straight wall cartridges cases such as 45 Colt or 45 Schofield, etc., simply will NOT EXPAND to fill and seal the chamber. Some powders DO create more soot and carbon fouling than others. However, it's the chambers that allow it to create Blow-By. Your going to get Blow-By. Some will just be worse.
Your best performance will probably be with Bullets around the 200Gr point. Going up in bullet weight will probably accomplish nothing more than increasing recoil. Going "light" will mostly result is bullets that tend not to stabilize well and wander around. Shooting CAS, at 7 yards, you won't notice much difference in accuracy. Out at and past 20 yards, accuracy will suffer with light bullets.
Were it I, I'd be lightly annealing my cases to get a good seal of the chambers. I already anneal all my Schofield cases for my 45 rifles. It works a treat. Most other solutions, especially those that suggest max loads of powder and 250Gr bullets are just not all that effective and in a hand gun won't be much fun to shoot. A little careful loading and bullet selection and you'll have a lot of fun with a Schofield.