You might try .50 Sharps basic 3 1/4 brass, yes, it is about impossible to find as well.

My early 1870’s Cogswell & Harrison .500/.450 #1 Express easily chambers the .50 Sharps case base/rim with a perfect fit.
Of course you do have to have the .50 Sharps 3 1/4” because the .50-90 Sharps is only 2 1/2” and thus too short.

If you can find the .500/.450 #2 Nitro Express 3 1/2” (equally hard to find), that will work as it is a thick rim. Possible that it might need neck reaming after sizing & trimming or maybe thin the rim to necessary thickness.

Generally the older BP Express chambers were a bit looser so don’t seem to need neck reaming or rim thinning.

Bertram does offer the ready to go .500/.450 #1 Express but it is currently nowhere to be found in the USA.

NOW: it IS possible to use the various cases like the .500/.416, .470, or .500 Nitro. You just have to headspace on the shoulder. Size a .470 or .500 just enough to close the action and fireform. The .040” rim is still plenty for reliable extraction.

- Mike