Where I got that July 1943 start date for the 2 Million block of serial numbers was from the M1icon carbine "born on dates" master list that I've printed off from one or more of the M1 Carbine Internet forums. That supposed master list shows every manufacturer of M1 carbines and it lists their assigned serial number blocks, with the supposedly actual build dates in parentheses along side each serial number block.

For Underwood serial numbers 2,352,520 through 2,912,519 it shows
(July 1943 - Feb. 1944)

I am not indicating that I believe that this is correct, but only saying that's where I got the July 1943 start date for the 2 Million block.