mountaineer,
First of all, welcome to Graybeards. You have a real nice rifle that will last a lifetime and then some. I have owned a G-Series .504 since the early/mid 90's. It would be easier to tell you what wont shoot out of a white .504. Seriously, about the only bullets that I don't care for out of the White, is the PowerBelt. They are made to fit in rifles with tight .500 bores and may not obturate fully into the rifling. The Whites generally like heavy bullets best in the 1-24 twist rifling. For conicals, anything all lead in the 400 to 500 grain, .503" to .504" diameter. Saboted bullets also shoot very well, the 435 grain White Shooting Star/Power Star shoot outstanding, but anything in the 250 to 300 grain arena can work with lighter powder charges.
Your Pyrodex RS will be fine, shot plenty of it in my White, although the Pyrodex P is a little quicker and aids in obturation. 777 FFg or 777 FFFg would be my first choice for the substitutes. You trying to sign in at DWB's as mountaineer?