Do some searching; there is data out there though some of it may have started out in paper manuals. If I chose to use .357 cases, I'd take .38 Special data and bump it up slightly with successive loads and shoot groups from a solid benchrest setup, chronographing at the same time. I'd go with what was most accurate for my gun.

I've never seen the carbon ring and I shoot only .38 Special in my .357 Magnum guns.