If you can find somebody with a .32 WCF (aka .32-20) chambering reamer, who also knows how to use it, you can have him rechamber your cylinder for that caliber. Very little metal is removed, to accomodate the slight .32 WCF shoulder. (The Nagant round is almost a straight taper.) Then finding ammo and reloadable cases is much easier.
It handles the .312" to .314" .32-20 cast lead bullet just fine.
This is a strong gun, and the cylinder is made of very tough steel, far thicker and better than necessary for the basically useless Russian cartridge. They are also very accurate.
I did mine, with an expandable hand reamer which was much less than ideal, but it worked. Nagant cartridges could still be fired, but they would be fire formed to .32 WCF...just before you throw them away.
There were a few adjustable sight target versions of the Nagant imported. One of those, rechambered, would be an extremely accurate and fun revolver.
Be aware that, among imported surplus Nagant revolvers, there is considerable variation in the tolearance between the rear of the cylinder and the recoil plate. Some cylinders might have to be slightly modified, or recessed, for .32 WCF rim thickness, but probably not.
The Nagant is one of the best values on the surplus market, except for the worthless, oddball, grossly overpriced, and rarely available cartridge...as you have discovered. You have a gun that is well worth the effort to make it practical to shoot, but most folks don't know this is possible.
Somebody was also selling a .32 ACP cylinder for these, at around $80...which is close to the cost of the entire gun. But this is hardly worth the bother, compared to what you can get out of .32-20...which is one jump upward from .32 H&R Magnum, although I don't load it that way in an older revolver...my Ruger Buckeye Special being a notable exception.