buckshott - I will check out my Brophy Springfield book. It has a fairly good breakdown. The following is what I remember:
I know that the 1941 Remingtons were virtually identical to the Rock Island 1903, and I understand that continued into at least early 1942. At some point late in 1941 to early 1942 Remington modified some of the machined parts to be stamped sheet metal, and referred to it as the 1903 Modified. Most of the 1942 production was 1903 Modified. Near the end of 1942 Remington was building 1903A3's, though there were enough parts still in the pipeline that some 1903 Modifieds were still coming off the line, up to December 1942. All 1943 Remington 1903 production was referred to as 1903A3's.