One thing comes to mind.
If you aren't getting the accuracy you prefer out of the Nagant why not try a modern smokeless powder (H4895 comes to mind) and work up a load like any other rifle.
Also, what happens when you find the sweet spot for the load using the powder from an unknown source ? Are you going to pull, reweigh and reload every round in the future ?
Keep the milsurp for blasting, clean up like the folks here suggest and keep the brass for working up a tackdriver load that you can duplicate.
You might find a great load for the current case of milsurp, but next case could use a completely different powder.
In any event, how much accuracy is a Nagant capable of delivering ?