I suspect you will find the national command authority missions (naoc/looking glass/night watch/neacp etc E4 and E6 flights) will have two word callsigns, such as DYNA TRON and YEW TREE and so on. Their corresponding ground stations might also have two word callsigns, however they will really be Offut, McClellan or some other AFB in disguise. I don't think the E4/E6 flights have the ability to key up hf remotes at the various AFB, so when you hear a test count, that's a radioman (or woman) at some AFB.
Here's some further info on (specifically Offut) AFB hf ground stations;
http://www.offutt.af.mil/News/Features/Display/Article/312829/rural-communications-site-has-global-mission/https://www.facebook.com/Det2Elkhorn/The Scribner (50 miles nw of Omaha/Offut) comms site mentioned in the first article was a huge air base in ww2, with enough landing strip for the B29s. It's near Scribner Nebraska, way out in the sticks where the local rf noise will be really low.
I suspect the Elkhorn site is the tx end and Scribner the receiver site due to the fact that I once copied a Spanish Lady bcast that must have originated at Elkhorn due the signal level and stability - I lived only a few miles from the site at the time. Scribner was also used as an emergency landing site for the shuttle program, and is alleged to be a site where potus can land in time of national emergency. I think I recall part of the Scribner strip is now a drag strip on the weekends.
https://en.wikipedia.org/wiki/Scribner_State_AirportThere's also a old inactivated nike or other air defense missile base north of Omaha around Arlington (I think, not sure) that last time I drove past still had wire hf antennas up, it may be a backup radio site.