Very interesting hypotheticals, Mickey, though not so hypothetical to some of us!!
I shall attempt to add a bit more of a parochial Australian perspective to 500Nitro's somewhat succinct comments:

As many of you will know, I already own a double rifle built by someone else on a shotgun action. I happily shoot and hunt with this firearm without a hint of doubt that it is up to the task, for several reasons:
1. I know the gunsmith, Rolph B_, who built the rifle, he has made several and there has been no problem with any of them to my knowledge.
2. I know the fellow who originally commissioned the rifle, Les O_, and he is no fool. He bagged either a scrub bull or buff with the rifle before passing it on.
3. I know the chap who bought it from Les, and from whom I acquired it, Tim_ had used some heavy loads of fast powder to boost performance, without detriment to the rifle.
4. I know that the uniquely Australian (?) practice of proofing the firearm by firing a full load with a heavily case-lubed cartridge, at the very least, would have been adhered to in the first instance. Right or wrong, this is generally believed to increase the back-thrust by 15 to 20%. Once I had settled on a regulating load I did the same. Passed with flying colours.
5. That other accepted Australian practice of shipping the gun for inspection and test-firing prior to the sale also allowed me to take a good look at the workmanship and critical dimensions before giving it the nod.

Without all these ducks lined up, however, I may have been a little reluctant. If I didn't know the maker or previous owners, or suspected any impropriety, no way!

Regarding rechambering, I believe each case must be judged on its own merits (pardon the pun!) Ruining a nice .360 by rechambering to 9.3 is in most cases a travesty in my view, however rechambering from .458 to one of the .450 NEs could be viewed as a salvation! Upping .375 NE to .375 Flanged Magnum is more of a grey area !

I would probably be content with a .458 rechambered to .450 without reproving, as I would do it myself as specified above. If the dimensions of the gun were generous, and the price was right, I would be prepared to take the risk as both back-thrust and peak pressure should be lower than the original chambering. Regulation is another matter, either it regulates with the new chambering or it doesn't! Probably a 50/50 chance in the case of the .458 to .450 conversion. If I was unable to test-fire the rifle, price would have to accommodate the worst case scenario, ie re-regulation.

This response ended up a bit long-winded, apologies. Should have gone hunting today instead!