This is going to be long winded, but will help in the understanding of the transition from the American production to the Russian Contract production:

First, I wasn't the one to coin the First, Second and Third Issues for the First Model No. 3 Russian contract revolvers, but I use it because it makes sense.
The way I look at it is that the use of full serial numbers set a precedent for S&W military contract revolvers. The original Americans and the early military contract revolvers were marked with assy. numbers. This is acceptable during the manufacture of a revolver in the factory, it assures that those hand fitted parts are put back together correctly after bluing or plating. However a master assy. number under the grips means that when a group of soldiers get together to clean their revolvers, there is no visible reference on the front half of the revolver to match it back to the original frame of the revolver for reassembly.
The Russians appear to have not liked this and asked for the change. It would not have been a S&W change as they would have seen no reason for it. It is to be noted that the subsequent contracts of the Number 3 for other military entities were manufactured with full serials instead of assy numbers.

The Russians asked for basically 10 mechanical changes and one marking change before the beginning of production, the serial/assembly number change at about serial 500 and then 2 more major mechanical changes after production seriously began (approx 2500 pieces completed and an additional 500 in process). Examination of the 2 known very early contract revolvers shows that all of the 10 initial mechanical changes seem to have been implemented at the start of production, not introduced during production.
As always, it is difficult to draw conclusions with so few surviving examples.

The original preproduction major marking change was the roll stamped Cyrillic address and double headed eagle inspector's acceptance mark on the barrel rib instead of the address and patent dates in Latin letters. Once established this mark would remain unchanged through at least the first three Russian contracts. Serial number locations would also remain the same for at least the initial 3 contracts and then the barrel serial was moved to the top of the rib between address an inspector's mark.
Joe