I used to shoot Winchester SR primers in my 357s for heavy silhouette loads. By heavy, I'm referring to heavy loads of slow burning powder under lighter weight bullets that I used to flatten the trajectory of my loads for Field & Hunter Pistol classes, which are fired out to 100 yards maximum. Being an iron sight Luddite in those days (while shooting production class) I loaded very hot 110 gr loads to minimize sight adjustments. SR primers did work perfectly for me except in revolvers with lighter hammer springs, but it was necessary for me to develop my loads from scratch for safetys sake. I never did try this with faster burning powders, but I was using powders like H110, WC820, and the like. My particular loads were over published data, so I won't disclose them.
My GP100 shot them well enough to be competitive, but I was outclassed by the guys with Contenders in specialty calibers with high magnification rifle scopes. Their scopes alone cost more than my revolver did. I did generally win in Production Iron Sight class though. I switched to a 357 Contender my last year and shot the same revolver loads in Production Iron Sight class with great success.
For your situation, I'd probably stick with medium to slower burning rate powders in the range of Unique (for example), and experiment a bit to find what I like. I ended up with a bunch of Remington 6-1/2 SR primers a few years back and am still using them for heavy ball powder 357 magnum loads. One thing to remember is that rifle primers have higher brisance than SP primers and will change the way your powder ignites in the case. This could affect accuracy, and consistency slightly. As a side note, I know a number of guys who use SP primers in 9mm, 38 Super, and 357 SIG with no apparent issues, but once again, these guys did their load development to work with the changes.