Where are you now?
We know that migraciones has a jail at Retiro. Do they have jails in every Delegación de esta Dirección Nacional en el Interior del País and do any of them have a history of detaining foreigners who go there to pay an overstay fine?
In another thread Dr. Rubliar explained that migraciones (at least in Retiro) detained some individuals with overstays while they sent someone to verify their address. I'm not sure about other delegaciónes. It might help if you indicate which one you are closest to.
As of June 17th Brasil will no longer require the visa for foreign tourists from the USA, Canada, and Australia.
The 100 year old VISA reciprocity policy has come to an end in Brazil. Brazil Ends Visa Requirements for Visitors From U.S., Other Nations
www.baexpats.org
Like you, I'm not sure what other similar border crossings there are
If you can wait until mid-June, Iquazu could become an option for leaving without paying, especially as it appears possible to walk across the border there.
If you can't pay the fine online as Dr. Rubilar suggests, paying at EZE could be considered "safer" as you will actually be leaving within a few hours of paying the fine.
Whatever you do, be sure NOT to pay the fine more than ten days before you leave.
Hopefully, someone will know about the procedure at the border crossings if you leave by bus and post about it soon.