I'm impressed that the OP openly came in here with his pants down, as it were. He knows he is 100% at-fault in this, but was hoping that there was some way / trick / secret handshake to retrieve some of his lost Benjamins -- and that's perfectly normal. Sadly, he drew the short straw on Delta agents and got one that towed the party line like a good automaton, which isn't necessarily a good or a bad thing... it just "is."

OP could have manufactured a story about how he was holding the head of his dying platypus while being overcome with grief, causing his tardiness, and the Dark Overlords at Delta ripped out the pieces of his broken heart and stomped all over it at his most despondent moment -- but he fessed up that he overslept, which takes a certain fortitude.

While not much could've been done, I would think the moment he awoke from his slumber he should've immediately called Delta and let them know instead of waiting until the flight was missed, which likely removed some of the options an agent may have had at their disposal to help him out.