Either the BRNO ZKK602, the CZ 550 Magnum, a BBK-02, Dakota M76 African, or one of the Magnum Mauser 98 actions from the Famous Amos makers,
any would be far easier to get up and running as a working rifle.
More work ahead if you want to use a standard M98 action.
Your barrel description did not include twist rate.
CIP 508mm or 1:20" for .500 Jeffery.
Go with the CIP .500 Jeffery for most universal standardization.
D. J. Lewis had W. J. Jeffery Rifle with serial number 25356.
Barrel was 24" long. No muzzle diameter specified.
It had a measured twist rate of 463.55mm or 1:18.25", 7-grooved.
I used a stainless McGowen No. 6 "Light Target" standard contour, 1:20" twist, 8-groove.
It finished up at 24" length having 0.820" diameter at the muzzle.
The 1.200" diameter cylinder shank ("Knoxform" if I wish) was 3" long then a straight taper to the muzzle.
Plenty heavy on a CZ 550 Magnum action.
Bertha will be about 11 pounds in a heavily reinforced laminated wood stock.
For a standard M98 action I would want a Sterling Davenport job like this one, found at a previous link on this thread:
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Sterling Davenport built the .500 Jeffery sort of like a .500 Schuler -Jumbo/12.7x70mm on a standard M98. Vertical stack magazine, different bottom latch.
He also did them on standard M98 actions with staggered-stack, drop-belly magazines,
like the one I got to shoot in Oklahoma.
I wonder which chamber this rifle actually has and what year it was built ?
Sterling Davenport mastered the ".500 Jeffery."
Rifle above has a 21" barrel length, 0.845" diameter at the muzzle, Mag-Na-Ported.
Rifle weight is 9.46 lbs. Yippee-ki-yay.
CIP homologated the .500 Jeffery on 12 January 1999, revised 15 February 2000.
It matches the 1928 Kynoch drawing.
CIP homologated the 12.7x70mm (.500 Schuler) on 27 January 1999, revised 20 April 2000.
It matches the 1940 RWS drawing that must have been copied from Richard Schuler's specifications
that surely existed before 1927 as the ".500 Schuler-Jumbo."
Shucks, I was having two .500 A-Square rifles built in 1999,
one on a BRNO ZKK 602, and one on a Ruger No. 1.
It is about time I got Big Bertha the .500 Jeffery shooting.
I am going to offer to apprentice with the gunsmith to help him with his backlog.
That might motivate him to finish it before I "apprentice."