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Leigh,
I have not analyzed this in detail, but let me open a possible solution
to any apparent energetic paradox:
Perhaps this is another example of an interaction in which the system as
defined must lose energy to the environment.
Also, I see nothing in your calculation that the requires that the force
of interaction be friction - it could be any mechanism. Perhaps you are
showing that that mechanism (even if friction) must involve a
dissipation of energy to the surroundings. (recall the "capacitor
conundrum").