2500fpm in an MD82 seems wholly consistent with all this.
Why was it overland by the Columbia/Venezuela border on a flight from Panama to Martinique? Could not all have survived if he landed on the sea, especially if he had altitude to position it by a beach?
I'm not sure they could do that. The accident occurred around 02:00 AM LT and it was quite impossible to make a safe emergency landing on the sea using a rate of descent described above.
However some years ago a Varig B737-200 made an emergency landing after losing both engines during a night flight over the Amazon rainforest. Several people survived including all crew.