I would have a look at .50 3-1/4" Sharps maximum loads for the Shilo rifle, for a starting load for your rifle. They should be putting a 500gr.+ bullet out of your longer case at about 2,000fps to start, so probably aren't too-far off where you want to go.

AA3100 and AA4350 are used in the Accurate Arms data. These correspond similarly to Hodgdon powders of 4831 and 4350.

What is the groove diameter? How long is the throat?
lyman makes a .510 mould which casts about 520gr. at .512" in WW alloy. RCBS also makes a .50 cal. mould that casts a 540gr. bullet in WW alloy.
Lee can make custom dies to reduce those to .502" or whatever you want. I'd order 2 of them - one at .506" and the other at .501", .502" or .503". The size should be whatever size your fired (not sized) brass will allow to be shoved in with fingers - tightly. You need to measure the ID of a fired case to see what size the cast bullet should be. This size is usually the most accurate, 9 times out of 10 as it lines up the bullet with the exact centre of the bore the best and does not start the bullet as crooked as a smaller one in a sized case - that is, if you are looking for the gun's best accuracy.

Always lube the cast bullets, ie: fill the grease grooves with lube, before reducing their diameter in a sizer. That way, they will remain undeformed. I have sized .375" cast bullets and jacketed down to .366" without any deformation at all and so have several other guys now, using multiple dies from Lee. I simply used a die I reamed.

If sizing down .510" jacketed bullets, you might want to get 3 sizes of dies between .510" and .501" or whatefver the groove diameter is. Jacketed bullets should be groove diameter or perhaps .001" undersize won't hurt.