I'll more than likely go with the 470NE.
My interest in the 500NE was more for the novelty and collecting purposes, wanting a caliber that was a significant step up from 458WM rather than something that I would functionally use as intended (elephant).
Here in Canada , 470 ammo appears to be far more common than 450/400, although it costs about $100 more per box.
NS,
I've been following your thread because 5 years ago I was in a situation similar to yours, although you sound like you have more hunting experience than I did.
I wanted to go hunting in Africa, and I wanted to do it with a double. My only previous hunting experience was limited to the occasional pheasant, a few rabbits I shot as a kid, and a deer I hit with my truck.
To my good fortune, I found my way to Chris Sells of Heym USA and he graciously shared his knowledge and understanding of doubles. After answering his questions I purchased a 450/400, and I have absolutely no complaints. (I now own 6 Heyms)
If I may take the liberty of making a few observations:
You seem to have a lot of variables in your selection criteria - some of which appear to be in conflict.
My suggestion would be to determine which is most limiting and use that to resolve some of the others.
Your initial post was basing caliber choice on availability of factory ammo. I believe that has been put to rest - shoot hand loads - by any of the sources mentioned.
I would think caliber choice would be dictated by what you plan to hunt - you listed elk to cape buffalo and possibly (eventually an elephant). I know nothing of elk - but I have shot 3 elephants and 6 cape buffalo. My take, based on hunting reports, is - elk are typically taken at long distances, much longer than DG in Africa - especially with a double. My farthest shot on a cape was about 40 yds - my closest, a little over 10 yds. Likewise for elephant, 35 yds for the longest - 21 FEET for the closest.
While I shot a zebra at 75 yds with that 450/400, I don't see that happening often, and I don't see a shot at any DG - especially an elephant exceeding 35 yds.
I must point out - my 450/400 is strictly iron sights, same for the 500NE. I do know some guys put scopes on their doubles but I don't know if the Heyms are set up for it.
More than once you describe your double as being a conversation piece in your collection; with the caveat it could be used on North America's biggest game and eventually Africa. So, are you referencing bear, moose, bison, in addition to elk?
There are a lot of very experienced hunters on this forum who could weigh in on this: list the animals you intend to hunt, their typical ranges, and compare the ballistics of those 3 calibers.
Next question, if the rifle is capable of making longer shots - are you?
There is a post by rookhawk early on in this thread which brings up regulation and custom loaded ammo.
Do you intend to put a scope or red dot on it, or shoot it open sights? For me, personally - I would not put a scope on either of my doubles, (or any double) - I'd use a different rifle.
Yes, I know there are a lot of guys who do and hopefully will chime in - because it might help you solve one of your criteria by adding some range, but might also limit actual rifle choices to those which can handle scopes.
I've waited until last to broach this subject - cost:
Good doubles aren't cheap and cheap doubles aren't good.
You brought up the cost of ammo a couple times. Start there, availability for those 3 calibers is solved by custom loads. That also resolves accuracy and consistency issues.
If you're trying to solve that piece of the puzzle with factory ammo - don't, you won't like the result.
Define your shooting criteria, and be realistic - I doubt any PH will let you take a 150 yd shot an elephant, even though it might be as close as you can get to an elk.
Each of those 3 calibers will kill any of the game you've mentioned - provided you hit them in right spot. Shot placement trumps caliber, a 500NE in a leg vs a 450/400 in the brain.
If, cost is the limiting factor - set that as your limit and find the rifle which checks as many of the boxes you've set.
It would help if you eliminate some of the non-essential ones - wow and conversation piece, and accept the important ones - custom ammo.
Go shoot some examples of as many as you can, and I guarantee you will eliminate some choices.
There is a commonality in most of the responses - they tend to be positive with respect to caliber. Each of those hunters has found what works for them. You could sit and argue caliber for days, but in the end - the answer lies in your success.
Don't worry about impressing others with your choice, choose what works best for you.