Mate the amount of time and money spent on looking for obscure cartridges, instead you could buy some basic reloading gear and reload for anything and everything you could ever want.
Aye !!!
The simple SAAMI .458 WinMag will meet all your requirements if you will handload !!!
Allow the COL to exceed 3.340" by just a wee bit,
and allow the pressure to go as high as they allow the SAAMI .458 Lott MAP.
In fact if you just put a SAAMI-chambered .458 WinMag into a 3.6"-magazined rifle action,
and load it to .458 Lott COL and MAP,
use the max .458 Lott loads for starters and work up, or down, from there, you are done.
The throat on the SAAMI .458 WinMag allows it to be loaded to .458 WM+ levels that will beat the
tighty-shorty-throated .458 Lott.
The .458 WM+ will have higher velocity or lower pressures or both.
Before I gained this common sense, I experimented with the .500 A-Square X 2 rifles, and three other 50-cal wildcats of my own design, also X 2 rifles each.
My favorite 50-cal after all is said and done is the .500 Mbogo 3-Inch,
based on basic cylindrical .416 Rigby brass left long and necked down to .510 caliber.
It is a few grains of water bigger than a .500 NE 3" and a few grains smaller than the 500 Jeffery.
My starting load for the 500 Mbogo (second rifle) was 100 grains of H4895 with 570-grain XLC or TSX.
I loaded 20 rounds of that for last weekend's Western KY DR&BB Shoot, last Saturday.
Only 9 were fired there.
The remaining 11 were chronographed with a Garmin Xero the next day, last Sunday.
MV average from 23" barrel = 2258.4 fps
Std.Dev. for those 11 shots = 7.8 fps
Range temperature = 59*F
That'll do ! Excellent when the Std.Dev. in fps is less than the number of shots fired.
Like a bolt action "500 Rimless NE 3-Inch" of sorts.
With higher velocity or lower pressure or both compared to the 500 NE 3-Inch.
H4895 is pretty temperature insensitive, good Thermo-Ballistic-Independence (TBI).
I can use it for reduced loads with no filler or compressed maximum loads.
That is like from 60% of net fill to 110% loading ratio, if I dare.
My Norma 500 Jeffery brass has about 161 grains H20 gross.
My Quality Cartridge 500 Mbogo brass has about 156 grains H2O gross.
Here is a listing of algorithm-calculated "relative" case capacities according to the RCBS
CARTRIDGE DESIGNER TOOL, gross water capacity in grains:
505 Gibbs ................................. 186.3
500 Jeffery ............................... 158.8
50-140 Sharps 3.25-Inch .... 157.3
500 Mbogo 3-Inch ................ 153.5 (my wildcat)
500 NE 3-Inch ......................... 147.4
500 A-Square .......................... 146.8
500 Bateleur 2.7-Inch ........... 136.3 (my wildcat)
12.7 x 68 mm Magnum ....... 133.4 (my wildcat)
495 A-Square .......................... 133.1
500 Van Horn Express .......... 129.7