The first option you were given is not correct since the law says that you can only remain in any Schengen country for three months in a six month period. If you leave the country, you won’t be allowed entry for another three months.
Extensions on tourist status can only be given by the Aliens Police (Bureau) in the area where you temporarily reside. For your convenience, we’re attaching the relevant handout on residence permits.
Please note that the stamp you were given in Munich is your entry into the Schengen zone and movement within it is free. We suggest that keep your ticket and boarding pass, showing your trip to Greece, until your return to the US.The attachment goes on to explain that illegal extensions beyond 90 days will result in fines ranging from 600 to 1200 euros, depending upon the length of time over-stayed.
It also states that the fee for extending for over 90 days and up to 6 months is 464 euros.
Sooooo....I guess I need to either delve into what I assume will be a very frustrating and costly process of trying to get "legit", or decide to stay well under the radar until my six months is up and then just resign myself to the possibility of a fine upon exit. The latter option would also negate the possibility of any trips abroad to any of the other Schengen countries.
A third option that I think should be adequate would be to take a trip home to the US before my first 90 days is up, thereby getting removing me from the Schengen zone and starting my 90 days over upon return.
Something to ponder while at the beach today...