I've got a few rounds of the Mil-spec ammo. It was made under contract for the Airforce by Winchester. It is nominal for commercial brass in the .22Hornet.
I'd suggest not shooting it. If it is still in the original boxes and wrappers, it's much more valuable to a collector. Its FMJ bullets make it unsatisfactory for most Hornet use. Save IT !!!
The most accurate .22Hornet ammo I've shot is the RWS and Hornady. Some Sellier&Bellot was also very accurate, but velocities were very mild. (2,450fps w/45gr SoftPt. bullets.
I've not had much luck with accuracy in the NEF's.
I'd look for something like a CZ527, or perhaps the new Remington 599 (mini-mauser) if you are wanting a .22Hornet.
Perhaps the Savage 40 if a single shot is acceptable.
I've had a number of Hornets. The one I had in the H&R Topper was NOT accurate.
The best Hornets I've had are a T/C Contender, Ruger M77/22KBZ (has "issues", but has been "made" to shoot decent- lots of work....); a Ruger 77/22 Blue Carbine.... couldn't be made to shoot!!!!!!, and a Ruger #3 that someone botched a .22K-Hornet conversion on.
My next Hornet will be either a Savage 40 w/accutrigger or a CZ527. Hopefully I'll escape my Hornet "jinx".
To get the best and most from a Hornet, you really must reload for it. I've been reloading for mine for 40+yr's. I REALLY, REALLY like Hodgdon Lil'Gun and a 40gr Sierra Varminter H.P.
Try to get you some Sellier&Bellot brass. You'll have to turn down your decapping stem as they have much smaller flash-holes than U.S. spec. brass, but with small pistol primers, the velocity variations are much, much lower and accuracy much better as the brass is very uniform, especially in the necks.