Unofficial, private purchase examples:  

I believe you've got it.        

Just happen to be drinking a bottle of Kirin, amusing to see those labels. Luckily I can find Kirin every once in a while over here, it does tend to be on the expensive side though,  Some amazing pieces in the collection, its really luring me into hunting for some pre WW2 goodies. The variety of insignia and the uniforms just hit different in my opinion. 

Its on baystate state militaria they are usually good about keeping the listings accurate. Although they do have it listed as a engineer cord so I guess i just did contradict what I said. I know the leather chin straps in good condition are rare to find. Especially an early private purchased version. I'll just get a repro for the time being to have something for display. But thanks for the help.

Some nice pieces in there, I'm rather partial to pre ww2 aaf collar devices and love the 5th bombardment group DUI, missing one myself. Do I see some unusual bullion parachute wings in the first image? 

As EE87 posted earlier, here is the unauthorized Combat Mortarman Badge:     I don’t yet have the unauthorized Combat Machinegunner Badge that this company, Goons Up, made.

They look good, but I sometimes have trouble delineating WW1 from post-war manufactured hat cords.

This photo looks to have some of the same people in it. Fort Mojave did use Mojave's as scouts.

I didn't know that about the hat disks, so its complete fantasy when coloectors claim its correct for ww1. But you are right so many collectors do that with campaign hats. Regarding the cord would this be correct for medical department? I don't think its engineer it doesn't appear to be the same color. Unless the red faded over time.

Living in Montgomery in enjoyed the post card.   Great research and thanks for posting the hat.