I dug out WRACo Vol 1, thinking to find the answer, but found no reference, except that Winchester-made bullets were marked with a small "w" until 1932.  HWS Vol 1 reports that "Navy contracts for Cal .30 ball ammunition continued through the 1920s and into the early 1930s. An illustration shows a WRA 31 headstamp.   Later in the same long paragraph, the writer reported that some of the contract ammunition was released to civilian shooters via the National Board for the Promotion of Rifle Practice.  The last sentence in the paragraph reads "A late ball round, headstamped W.R.A. 30, has been examined with a nickle-alloy or monel metal primer cup - possibly for subcaliber use." 

In December 1961, I was assigned to inventory ammunition in storage at the Naval Ammunition Depot at Lualualei, Oahu.  I was amazed to find .30-40 cartridges in service.  They were Model 1925s, loaded with 172 grain M1 ball bullets.  The boxes were marked for subcaliber use and had Frankford Arsenal labels.  The cases were headstamped FA and dated from the late 1920s.

After all that, I don't think the cases are original to the box.  The box would have contained cases headstamped "WRACo".  After all that, the box and cartridges are still an item of interest.