Rotating counters should already be possible with a technique similar
to one you describe. What you can do is create a piece with six sides
(for hexes, four sides for a grid). Just take your original counter
image for the first side, and rotate it by 60 degrees for each
successive side. Then you could set your tap action to increment the
side to rotate the piece. You could look at the "gunner" pieces in
PiratesVsNinjas for an example.
Adding a new piece action to rotate pieces inside the game (so that
the EveryGame handles the rotation instead of you making the rotated
images outside of the game) is in the plans for a future release too,
though I can't promise when that will be.