.45 Colt ammo has a bullet nominally .455". A .410 is the only shotgun made by caliber, not gauge. That is why it has a decimal point ahead of the number, whereas 12 gauge, etc. does not. It should measure .410 inch. What does that tell you?

Also, the steel in many older .410's is not intended to handle high pressures.

I do have a very old (1920's) .410 by Iver Johnson or H&R that is marked for .410-.44 ammo. I have no idea what .44 they meant. .44 Russian and Special bullets should be about .429-inch. But I'd never risk firing them in that gun, still less .44/40, which is nominally .427 inch.

If you want more power in a .410 than shot gives, fire slugs, not pistol ammo. (I think there are .410 slugs ?)

I am not an admirer of the Judge and the Governor type arms. As far as I'm concerned, they should be impeached.
But I'm pretty sure they are made to handle much higher pressures than shotguns are.