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Hi Bill!
I see your purpose! I would still restrict the word "static" to mean
independent of time, not just a snapshot of a time dependent phenomenon.
We can save the day by observing that the DC current situation is a
hybrid combination:
Once the turn-on transient period is over, a static (unchanging) charge
distribution has been built up (and will be maintained) on wire surfaces
(and anywhere there is a spatial change in conductivity). This static
charge makes the electrostatic field which drives the current. The
charge distribution and the fields are static; the charge carriers are
moving - some call the entire situation a quasi-static situation.