Concerning Schoolbd's rifle, it has been produced between 1936 and beginning 1940, 1936 because of the« oval » loading-ejecting port and beginning 1940 because of it's BUG proof mark.
The earliest ES340B s/n are around140000 the latest just below 2xxxxx (the 2xxxxx was more than probably a special range for Mm410B). This s/n 140000 to 199999 range also includes ES350B.
The highest s/n that I've seen in the199xxx range is a ES350B s/n 199896 for sale in France (Why didn't I bought it ? Knowledge missing when it was for sale).
I've never faced any ES340B or ES350B with a 2xxxxx s/n. (2xxxxx was dedicated to MM410B as far as I know. A few ES350B were made with 30xxx s/n, all eagle proofed, around 800ex as far as I know.
Dating a Mauser's 22lr production is impossible (for me, waiting for the clue...!) as I'm not sure that all the produced ones were sold (a lot of them were found in the inventory by french occupation army) and also as the sales informations given by Jon Speed: after 1930, they are from September to October (Mauser's archives) not anymore from January to december.