2 August 1937 - Barrel, P/N 28286, this is the barrel for the gas trap
10 March 1939 - Barrel, P/N 13661, this is the barrel for the front end shown in post #3, the gas port is 0.069"
1 March 1940 - Barrel, P/N 35448, this is the barrel that would be produced until the end of M1 production, gas port diameter 0.079"
1 March 1940 - Cylinder, P/N 35449, this is the narrow front sight base type gas cylinder, used until 1943-ish.
So, yes, in June 1940 production would have been with Barrel, P/N 35448. However, in the summer of 1939, 200 rifles "of the new front end design" were shipped to the Small Arms School at Camp Perry, a few weeks later another 200 were shipped as some of the original ones had problems with the cartridge follower. The fact that Springfield could ship 200 replacement rifle of the new design, along with the 200 shipped to Fort Benning for testing (along with 40,000 rounds of Ball, M2, Lot # FA 3047) that quickly, shows that this intermediate design was not a one-off, or prototype, but something in production. There are also excerpts from letters from 11 States', as well as the Hawaii and Puerto Rico National Guard of their opinion of M1s with "the new front end design", so at a minimum 51 other M1s of the intermediate type, more likely 510 (ten to each NG command). M1 production with the second type gas cylinder had to be fairly substantial.
In any case, all testing of the new front end (non-gas trap) was done with M2 Ball. The entire report is several hundred pages long, so no, I am not going to scan it, you can look it up, I will however show you that the new front end was tested, and optimized for Ball, M2, not Ball, M1.