After going thru the whole thread and putting the trail of info from the op in a number of posts this is what I have gathered in terms of goals, gun use, range, and secondary gun you will have access to.
Ideal barrel length: 20"
Caliber minimum: 30 cal or larger
Min bullet weight: 180gr or more.
Hunting location: Alaska, International(Asia, game Abex)
Max distance: 500- 600+ yds
Backup Gun: Short distance brush /charge gun 416 Ruger Guide Gun
Current Armory Inventory: traditional barrel lengths in a few .338’s, a .300WSM in a Kimber, and a short barreled (20”) 7mm WSM.
IMO, as you reduce fairly short barrel lengths for a given powder volume there are benefits to be had by increasing caliber size as it helps offset the loss of bore volume and can regain loss energy by the increase in mass in a comparable ratio..
If there is any ofbthe thick skinned African game that has min caliber restrictions you would be stuck to .375 up but given your stated experience I will assume you know this and would have stated it.
The main thing is possible 650yd max possible shots with a case shooting 30 cal and larger with enough velocity for an ethical kill in terminal performance from a 20" barrel. In terms of the Ibex I have seen numerous kills posted using a 300 win mag 24"-26" 180 gr to 400-450 yards results being they flopped right over. So to me it seems ideally we need to equal the terminal perf of a 24" 180 gr 300 WM @ 450 yds but from a 20" @ 650 yds.
RUM would get you there but its a very long COAL especially if bullet is ideally positioned in case neck. The Norma Mags fit the bill well as they have that great ratio of case diameter/length and will work with wyatt and DBMs. The other choice would be a Nosler Magnums
If we go with a NM that of course needs the .590 face/.750 lug bolt action. The Nosler uses standard mag .532 bolt.
My opinion from my knowledge would be to lean toward a 338 given the short barrel length. A 338 bore 20" has 98% of the bore volume of a 24" 30 cal. So for a given powder volume the 338 in a 20" will burn as efficiently as a 24" 30 cal all things equal.
Looking at some of the most experienced long range elk hunters on this forum they seem to indicate, that even taking into consideration of the fantastic bc of the heavier 7mm & 30 cal bullets today, 338 seem to handle switchy winds better and hit with more terminal authority from their observations.
Based on all of this I would think a 33 Nosler or 338 Norma Magnum using an action compatible with wyatts cfe-9 or cfe-12 box respectively would meet your goals. Something like a 250gr EOL or similar running 2700-2775 using RL26 H1000 N165 N560/5 Retumbo @650yds will duplicate and/or exceed the 180 hunting bullets (AB, TTSX..... EOL) mv 3100fps @ 450yd perf