Those figures are interesting and educational. But there should be more rifles, and I think that the Ordnance inventory might not include the Navy or Marine Corps. Here are some other figures.
On 30 June, 1939, the entire U.S. Army was 187,893 men, of whom 22,387 were in the Air Corps. The National Guard (there was no Air National Guard) was 199,491 men, for a total of 387,384, so the figure of 306,514 rifles in the hands of troops in 1937 pretty well matches if Navy and Marine rifles are not included.
In 1937, plans for "full mobilization" envisioned an army of 250,000 men. Even by mid-1940, predictions of a 4 million man armed forces in the event of war were denounced as absurd and fantasies, but it soon became apparent that if the U.S. was drawn into a two front war, the its armed forces would have to be huge.
That is why the Army was deeply concerned about the availability of rifles in the 1940-41 period. The Army's major arms factor, Springfield Armory, had been retooled to manufacture the M1 rifle. Yet, by the end of 1940, barely 100,000 had been produced, and it looked like there could never be enough for an army that everyone knew would be vastly expanded.
In addition, in the fall of 1940, the president ordered 1.1 million Model 1917 rifles declared "obsolete" (to comply with international law) and shipped to England. (This was not "Lend-Lease"; the Lend-Lease Act was not passed until March, 1941.) Those rifles had been the largest part of the Army's war reserve, and now they were gone. It must have been enough to make Ordnance officers cry.
Those factors led to a greater urgency in getting Winchester started on M1 production, and also to the letting of the contract to Remington for Model 1903 rifles, supplanting the previous British contract for a .303 version.
Jim