the case is in fact a 577 basic with thinner and smaller rim, believe bertram make it. have seen from time to time double , around 3500$.
you can use any 500 BPE bullet and loading data. If you are more tricky it can be one of the cheapest cases for big doubles. take 2,5" magtech brass for 24 gauge, reduce the rim, stick a brass tube in and and resice.

From my book "Modern Gunnery" , Henry Sharp, 1906

W. R. .500 bore Double Express
Barrel, 28 inches for W.R. No. 2 Express cartridge
Charge powder, 125 GRS.
Bullet 360 grains
Muzzle Velocity, 1650 fps
Muzzle energy 2612 ft. pds.
Cartridge case 2 13/16th. inches

The .500 bore Nitro Express Rifle is as follows

Muzzle velocity 2100- fps
Muzzle Energy 5577 foot-lb.
100 yd. velocity 1893 fps
100 yd. Energy 4532
Cordite powder 90 grs.
Bullet 570 grs.
Rifle weight 8.5 to 9.5 lbs
Frank