9-44 SA is the latest Springfield barrel I've seen, but a 10-44 is possible. I have seen a 2-45 Sedgely barrel, which is the absolute latest.
Springfield continued to make M1903 parts through Fiscal 1945 (which encompassed the last part of 1944 and the first part of 1945), including barrels. I've always theorized that most of the parts were in the "1944 part" of that FY.
While M1903s were definitely on their way out, they continued to be used in "secondary" uses and, until Japan actually surrendered in August, 1945, there was no definite end date in sight.
"We make men without chests and expect from them virtue and enterprise. We laugh at honor and are shocked to find traitors in our midst."
--C.S. Lewis