The good news is that they are both within .0005 of each other.
The bad news is that it seems very large for a .577 Land + .580 groove = .598 Measured 30 minutes after cerrosafe poured into bore. What to do?

Mike:
It might be best to 'slug' the bore. Use a big lead fishing-sinker if nothing else is available, peen it to just oversize with a mallet (drop-fit into chamber), lube it, then drive it about 3 or 4 inches into the rifling with a stout dowel and the mallet. Then drive it back out, and measure. You can drive it all the way through, but some early rifles have a few points of constriction over the length of the barrels.

I don't understand what you mean by "Land + .580 groove = .598" On a bore-cast, simply measure across the 'lands', which are the grooves in reverse, so to speak. That gives you the correct projectile diameter.

I know you know this, I'm just not getting it for some reason. Apologies.

Marrakai, the .598 is across the "lands or reverse grooves", the ".580 groove" is the measurement across the reverse lands. The inside of the barrels on this gun are quite good. Isn't this a little large for a .577?

Marrakai do you know where I can get bullets to test in a gun with a true groove diameter of .598? Or will the stock .577 caliber (.584) bump up if cast in a softer mix?

I don't thing so. Your lead cast bullet has to be .598 in diameter minus thickness of 4 layers of cotton paper, which I'd strongly recomend you to use with BP. When you get the real diameter of bullet depending of paper thickness, some people prefer to use just a bit larger bullets in diameter any way and they say it's improve shooting. The lead bullet hardness could be 5 (pure lead) or for .577 DR I'd personally prefer hardness 15 (wheel weights lead, clip on + 2% of tin, hardened in water).
If you 100% sure your .577 DR has .598-.580 grooves and bores, you could ask machinist to increase internal diameter of mold to needed size.
I made for myself several bullet sizing dies to get different bullet diameters for using with paper patch or without and I have to say it's very helpfull.

Thanks Geno. I am going to load nitro for black. I hate messing withblack powder. I will probably have a custom mold made for a paper patch bullet. Seems the way to go.

Does anyone have contact info for mold makers that can do this? Thanks

The Civil War era Minie ball was a hollow base bullet that was designed to be loaded from the muzzle, and to bump up upon firing. Lee Precision sells a mold in .578 that might bump up to fit your barrel, and it would be just right to load with the unjacketed part way out over the rifling of a .580 bore. You might want to look at the picture on Leeprecision.com and see if you think it would work. $26 for a mold, handles included, beats the price of custom work.

I don't know if this will work, as I have never tried it, but I don't see why it would not.

Don't think so. First of all, I didn't find the weight of this bullet (500gr?), the weight of bullets and powder load is very important for DR regulating. Second, gases can burst through between naked lead bullet and rifling, the presure is pretty much high. Third, when use naked lead bullets, the bullet hardness depends on working pressure and lead hardness has to be high in this case. Paper patch is the same as bullet jacket and allow to use mild lead allows in high pressure DR.
And forth, I've allready steped on this rakes and strongly suggest to follow experienced BP or NFBP loaders recomendations.