I own Mosins converted to 8x57, .30-06 and .30-40 Krag.
I've also seen Mosins converted to .45-70 single shot rifles.
I own a rifle in the MN biathlon caliber 6.5x54r.
The 8mm is the Polish Wz.91/98/25, the .30-06 is a Bannerman converted "carbine", and the Krag is, I think, a one-off conversion. All have had chambers recut in shortened knoxforms that were reshouldered and rethreaded before rechambering, so the cases are properly supported.
I've frequently fired both the 91/98/25 and the Bannerman, albeit with cast lead bullets due to bore variations. Both function flawlessly, feeding effortlessly, with perfect extraction and ejection. The Polish rifle loads with Mauser stripper clips as easily as any Mauser.
All of these rifles have had extensive redesign and gunsmithing by their makers to get them to function properly.
Never have seen any proof of a Bannerman having problems, everything bad about them seems to be from gun writers but not gun users.
I've just received the Krag conversion so have not fired it yet.
All of these rifles were converted for various reasons many many years ago; the Poles, to standardise calibers in their fledging army before enough Mausers were available, the Bannerman's, well, just for profit, and who knows why someone would convert a MN to .30-40, perhaps to save money 50 years ago when Krag ammo was considerably more available than 7.62x54r.(?)
That being said, I've owned plenty of (standard caliber) MN rifles since the 1980s and have never ever had any problems finding 7.62x54r ammo to shoot in them, or cases and bullets for reloading, ever. I just cannot see why anyone these days would want to go to the trouble and expense of rebarreling or rechambering a Mosin to another caliber.
I own a few Mosin sporters in 7.62x54r and cannot imagine why any other caliber would be needed in a MN for deer, elk, feral hogs, black bear, etc., in North America.
I'd be leary of a conversion to a high pressure cartridge, such as 7.62 Nato, or any kind of "improved" MN round, as the rifle was not really designed for much higher pressures, and besides, most of the rifles around are very old.
If you want to shoot an "improved" MN caliber, I think you should acquire a Siamese Mauser action, which was built around a rimmed smokeless 8 mm cartridge, and rebarrel it to whatever Mosin variation you desire. The action is probably much stronger and safer,and the bolt is already set up for a round with almost the same rim diameter as a 7.62x54r. The magazine should also feed without problems, even a .45-70 round. Plus, most gunsmiths are comfortable rebarrelling Mausers.
If you want to shoot some other rimless caliber, well, you should consider rebarreling a P17 or a 1903 action, both of which can be had as butchered sporters in almost any gun or pawn shop in the country--no need to wreck a military as-issued rifle. Or just buy a new rifle in the caliber you want.