Has anyone from America tried this?
Yes, and plenty of them have been caught. The rules state quite clearly that you have 90 days out of every 180 - the existence of a stamp at the border doesn't mean a damn thing, it just means that you restarted the clock on that date. If you can't prove clearly that you're legally in Poland, then it's deportation and a year's ban.
You mean you Yanks deserve a red-carpet treatment?
I hope the Schengen states charge Americans for entry now that they're doing so for EU citizens!
And about the foreigners office - oh yes, it's great fun watching that ;)