I have just learned that the US Army Air Force marking started as a plain red star, then it changed to a roundel for commonality with other WW1 allies.
Two observations:
1. What would the Russian Airforce have done if the red star was not available?
2. I now know what the DH-4's markings are, in Kiwithrottlejockey's great photos:
http://www.pprune.org/aviation-histo...ml#post9612142