An update...
Well, I got the rifle. Here's what came of it.
It wouldn't chamber brass. Not Winchester (which I believe is Prvi), not S&B, not Lapua, and not Norma. As far as I know, those are the only four companies in the world who make brass for this gun. Surplus was also a no-go.
Additionally, the scope had been mounted on a set of rings that was too low. The hammer could touch the knurling on the objective ring of the scope when cocking/coming back down, depending on how the ring was rotated. Someone noticed this, as the bluing was a little chewed off some spots on the rings.
When I brought this up to the folks at Randy's Custom Rifles (very politely!), they assured me the rifle 'fed and fired' fine. Now, I'm not one to call someone a liar, but I had two questions. First, how does a single-shot rifle 'feed'? Secondly, if none of my brass chambered, how did they test-fire the gun? They assured me the scope was an item I had damaged, the rings were the correct height, and that I had custom, strange-to-fit brass. I did ask them to simply let me ship the gun back to them, but they demurred for a few days - despite the fact that I offered to pay for more work if I somehow was at fault.
I received no replies when I stated these doubts. I indicated to these folks that I was unhappy with their service - as I can put together a dinged-up, non-firing rifle in my garage for considerably less money - and they offered not a lick of customer service. Literally nothing. I do have emails, for those of you who may want to see them - I will forward them, as they are text-heavy, and I don't want to fill the thread up.
So, at this point, I can safely say I would never, ever give another penny of my money to Randy's Custom Rifles, of Wapiti, WY. I didn't chisel a penny off their price, and I got very little in return.
I then brought the gun to Lock's Gun Shop, in Philadelphia, PA. The 'smith there saw what was wrong, chatted me up in fine style, and assured me he'd fix it right up. He confirmed all the things I thought were wrong, and sent me on my way.
Three weeks later, I got it back. New scope, new rings, new chamber. The scope is a Bushnell Elite 3200 3-9x. It appears purty clear to my very untrained eye - my other two scopes - for comparison - are an AIM scout scope, which is surprisingly good for what it is, and a BSA Sweet .22. The rifle does have a nice synthetic stock. (I do also have the wood to go with it.) The whole thing is lovely. I've got a starting load worked up for it - Lapua brass, with 3.1cc (about 42 grains) of Varget, topped off with Nosler ballistic-tip 180's. Haven't shot it yet - I'll post when I get there. The .308 idea really is awesome, my bullet selections are SO MUCH larger than the .311 my Mosin eats. I would spend my money happily at Lock's again.
Enjoy some terribly-taken pictures, and thanks to everyone who pointed me in the right direction. I appreciate EVERYONE's opinion - even the dissenting ones - because you folks are some very, very, smart cookies!