Nice puzzle and an even nicer solution, yes. If anyone is interested I solved it this way:

SPOILER BELOW HERE!

Over time each coin will do a sequence of

  head - tail - x tails - head - tail - x tails ...

where x is determined by chance. Flipping a coin repeatedly the number of tails to expect before a head is 1 tail.

So on average the sequence of each coin is

  H - T - T - H - T - T ...

i.e. when stabilized 1/3 of the coins are heads up and 2/3 are tails up.