Format of In-Text Citations for Military Publications?
Apart from the guns and stuff, the United States Army is an organization just like the American Psychological Association. The United States should be abbreviated when it is used as an adjective and not when it is used as a now. When it is abbreviated, it should be abbreviated with periods but no spaces. Further, it does not need to be defined prior to using.

One then needs to ask who/what is the author and who/what is the publisher. If available, I prefer to use an Administrative (e.g., Headquarters Department of the U.S. Army) or Operational (e.g., U.S. Army Corps of Engineers) unit as both the author and publisher (unless the document has something more informative). See wikipedia for some possible units to look for.

This means in text citations might look like Headquarters Department of the U.S. Army (2016a), Headquarters Department of the U.S. Army (2016b) and U.S. Army Corps of Engineers (2016). Not that APA style is pedantic about making sure in-text citations are not ambiguous and has rules about how to handle "twin" (use a, b, c, ...) and "not-quite twin" citations (expand the authors until the ambiguity goes away while being careful with et al.).