Interesting thread, but my question is...what changed? Your stop "button" used to stop the engine, but it does not now stop it. Just a thought, but get a helper, and put a voltmeter on the terminals for the stop solonoid. On my 135's there is a relay mounted right there, which provides a full battery voltage to the solonoid from the main battery terminal on the starter. It takes less voltage/current through the long wires from the stop button using this "pony" relay. Much like your starter solonoid mounted on your starter. My starboard engine did what you are discribbing, and I noticed that there was not enough current to pull the solonoid all the way in for a full stop. The relay was bad...the relay is the little black, square thing, with 4 wires on it.
Again, just my two cents worth...DenO