Good ideas, thanks, but unproductive I'm afraid. Tried using Safe Boot in both my main account and an almost-virgin second account, as well as normal boot in both. The only thing that changed was that in the second account with safe boot, when the restart occurred with the Get Info panel for the TM drive open, I saw the TM drive icon in Get Info > Preview flash the correct green icon just briefly, after which the orange icon appeared. All further test results showed the orange icon in all locations except System Preferences > Time Machine. That was last night.
After an overnight shutdown, a normal boot into the normal account, Get Info shows the correct small and large green icons, but still the TM disk's desktop icon is the orange one.
Incidentally, when the orange icon is showing, it doesn't have the expected USB logo -- the orange area is featureless.
This isn't a matter of life and death, but there should be a solution somewhere.