Hope this little bit of information will help you further date your M1.
According to author Canfield and other books by Frank Iannamico the Savage Arms corp was the original
Developer for the simplified version of the Thompson, the M1.
production estimates from most books I see
Is about 464,800. M1and M1A1 from Savage.
AO produced about 249,555 M1 and M1A1.
I think M1 production started around April of 1942.
Officially from what I read Aberdeen approved in
Late October 1942 the M1A1 was authorized for
Production with the simplified bolt. Fixed firing pin eliminating the
FP spring and hammer.
January or so of 1943 AO placed the order with savage to
Build the M1A1. Not sure when that production actually started.
I know in 1944 some AO mfg M1A's were date stamped 44
Not sure if this practice was done in 43.
Also some M1's that were converted to A1 configuration were Hand Stamped A1.