Ok finchyboy - I have just called AA and checked on their policies - based on my own potential future interests after just returning from Honduras and finding loads of teaching jobs.
There does have to be proof of onward travel to anywhere on any airline IF, as Boomer suggests, they ask for it. Since "booked" suggests you've already got the one-way ticket purchased, you do have some options based on however your organization has worked out your being in the country.
None of the schools I specifically spoke with in Copán Ruinas got official work Visas for their volunteers, whom remained covered under the 90-day CA-4 Tourist Visa. They said that holiday breaks, etc. always managed to fall right around the cut-off period and volunteers either returned home or went to Belize or Costa Rica before returning on another 90-day Visa.
Perhaps that can work into what ever necessary arrangements you'll need to make. Otherwise check Spirit, Delta, Taca, Copa or any other airline that flies in/out of SAP and buy the cheapest on-going fare you can find to anywhere. Otherwise you risk getting stuck last-minute at the AA counter - and the only place they can get you from SAP is back to MIA.
The More I Go...The Less I Know ~
2019: Puerto Rico, Costa Rica, El Salvador, NYC, Croatia, Montenegro, Bosnia & Herzegovina, Istanbul, American Southwest Grand Circle, Los Angeles, Brazil/Peru Amazonas, Colombia.
The Ozarks and Buffalo National River area keep me occupied while home.