Russ,
With those measurements, it's very much a 577/500 No.2
When you say the neck is at 2.3", is that where the shoulder is or the point where the neck begins?
My 500No.2 neck is right about at 2.3"
Also, get a measurement of the rim thickness too. The regular 577s have a thinner rim than the No.2 and the base of the 577 is bigger.

Can you show the chamber cast?

Hoyem lists a nitro for black from Kynoch with a 440gr bullet and a charge of 53grs cordite.

I am unaware of a full nitro version of this cartridge but a full nitro version would be a great gun imo.

I have a full set of forming dies for this cartridge so if it is in fact the same case, I can run some brass for you. Not easy to find though.