If you think USSR sold all tools to China you don't feel what USSR was in reality. Even SVT-40 tools were put into "strategic storage" in 1945. I suspect they are still there in Russia. Until 1990x ex USSR amry storage facilities in Ukraine had tons of WW1 weapon properly preserved in grease and ready to be used, it was sold at scrap prices in 1990x mostly to German milsurplus dealers. Still some nice specimens can found. USSR did not scrap anything after the WW2.... you know, just in case with war with "evil capitalists" they would have needed to have AK for the army, SKS for the rear echelon units, SVTs for militia, MNs for partisans, Lebels and Madson MGs to arm polar bears to help "to liberate" Canada and so on.
It looks like letter series SKSs were kind of "additional" runs of production and as a proof of that - they were using both old stock parts (you can find both wood and laminate stocks) and newly manufactured parts. At the time of production they just followed year naming scheme that was already in place with cartridges and some other small arms. Take for example PM (Makarov pistol) - year was stamped up until 1955, then in 1956 they stopped stamping year and used suffix Д, and so on -
Д-----1956
И-----1957
К-----1958
Л-----1959
М-----1960, this year pistols could have either 1960 date or M suffix, but not both
----1961, this year pistols could have only 1961 date, no suffix was used
----1962, this year pistols could have only 1961 date, no suffix was used
----1963, this year pistols could have only 1961 date, no suffix was used
Р-----1964 this year pistols could have either 1964 date or Р suffix, but not both
Reasons behind using or not using such dating scheme is not know AFAIR, however information above is based on quite solid studies of cartridges and firearms and I have no reason to doubt it. This is the best information we have as for now. While with the theory that all letter series SKSs were made in 1956 all we have is "it's just because 1956 last year of production".