I'd also suggest OTL interwar Austrian uniforms for another source for the US military. Especially with the same kind of engravings being used for Union ceremonial helmets, only replace the Austrian eagle and flag with the American eagle and shield.
Some of these would actually look pretty good for parade dress uniforms! Especially in the Interwar Years. Just a change of color for the uniforms and, yes, of course replacing all appropriate insignia and medals with something more American would do the trick!
That last trio of uniforms there, of the post-war German Freikorps, is possibly the closest we can get to a TL-191 US uniform. Give it some US webbing and we're good.