I've only shot steel cased surplus through my Mosins but I've had great success with a few basic accuracy upgrades. It sounds like you are putting optics on these so I am guessing you wouldn't mind doing a few modifications that aren't collector approved? The only modification that would permanently alter these rifles would be bedding the action. I used acraglass to bed my M/N I bedded the rear tang and underneath the chamber but did not bed anything in between. If you don't want to alter your rifle in this way you can simply shim the reciever which I did using old stripper clips that I cut up. Also polishing the contacts on the trigger can greatly improve the trigger pull and of course accuracy. The best and easiest modification that I did to my rifles though was to use cork gasket to "free float" the barrel.

Pictures to clarify:

1. Cork Free Floating
I believe the Soviets did this with some sort of oil soaked cloth, but I just picked up some cork gasket at a local auto parts store and the result is the same with a lot less mess. I added 1 layer of cork underneath the rifle just in front of the end cap add enough layers of cork so that you can easily run a piece of paper from about the rear sight up to your cork addition. I super glued mine in place but this is not necessary. I also added thin strips of this cork to the front of my upper hand guard to keep it from contacting my barrel.

Hand guard



2. Polishing the trigger
I simply polished where the trigger spring and trigger itself contacted. I started with a fine grit sandpaper soaked with oil and finished it with a dremmel and a polishing compound. When I was done polishing and reassembled a put a small amount of grease where they contact.



3. Bedding the action
Like I said earlier bedding the action helped a lot and personally I used acraglass. I had never bedded a receiver before but the instructions that come with acraglass were more than satisfactory and it was quite simple and it only cost me about $20. If you don't bed you can shim the receiver which I've done before using stripper clips that I flattened and cut to the size I needed. I've used brass and steel stripper clips successfully for this. Some rifles come "pre shimmed" depending on when the stock was manufactured/rearsenaled. You will want to shim around rear and front receiver screws on both the top and bottom of the stock. You can also place a shim underneath the chamber.
Examples of factoring shimming


One of my stripper clip shims, ugly, but it works


I've done all of these modifications to my repro PU sniper and get surprisingly good results out to about 650 meters using surplus ammunition.
You probably didn't need all this information, but I figure accurizing Mosins is a pretty common topic and hopefully this helps you out and maybe some others down the road.