I would like to see either as you describe (which I think would be the most relaxing), or have the direction-changing buttons also count as a click each time they are pressed. I found it tempting to switch direction, turn a piece, then switch back, often using two clicks instead of the three it would take to turn it clockwise-only, but very inefficient since I switched back and forth many times. Making those count as clicks, though, does up the difficulty and would make hitting the target require you to use them only once, so perhaps removing them altogether is the solution.
If you did it as clockwise by default instead of listing the ideal turn count you could list the minimum number of “counter” turns. Then have a button to do the next turn as a counter turn.