AA wants you to enter your passport online ahead of time for international trips. Can it handle more than one there? If not, any issue with the OP using the Polish passport for the JFK-EZE but the US passport for the GIG-JFK?

Does the Polish passport, in fact, have to be used when boarding the JFK-EZE flight to dodge the visa / reciprocity? Or does it just have to be presented at EZE immigration? My understanding is that the $140 is paid upon entry at EZE (and btw last I heard not when entering Argentina in any place other than EZE!), not through the airline, which would imply that it's irrelevant to the $140 issue whether you used your US passport for the flight or not, just whether it's the US passport you show when entering EZE immigration.

(But I haven't been through EZE arrival immigration myself. I entered Argentina at IGU-IGR land crossing in late Nov 2011, and no $140 was collected there. They were surprised when I flew out of EZE that it hadn't been collected, but when they saw that I'd entered by land, there was no problem.)