Germans are not subjected to the new $130 fee at Ezeiza, so enter as a German, but remember: every time you come and go it needs to be in the SAME passport, otherwise there will be a gap and it will be suspicious and might cause problems (I almost got deported from Bolivia for something similar).
So, get stamped in and once your 90 days is up, get stamped out on that SAME passport. When you come back, if you want, enter as a U.S. citizen (since presumably you won't be entering at Ezeiza you won't be charged the fee). When your 90 days is up, get stamped out as a U.S. citizen, and then back in as a German. And back and forth and so on until it catches up with you, which very well could be never!