You can see a picture and description of a governed 2 stroke from 1917 here:
http://www.srhf.org/Antique-Farm-Engines-at-FHF.pdf

I don't think there is any suggestion that it was the first, it is just one that has been restored and documented.

The history of advancements and patents during and after the Great Depression I will leave to others, especially Cyberjack.