The only other option I can think of is to bus it to Izmir and catch a flight from there to ATH. But from my previous experiences flying this route A3 doesn't fly daily and flight times alternate between morning and evenings, so don't know if that would fit your needs.

No ferries to other islands AFAIK! The only other option - one which I once did myself - is to entertain yourself while on Kos. I did something similar on Chios after travelling in by morning ferry from Turkey: I just took a rental car from the port, put the baggage in the boot, and went touring on the island for the day before catching an onward overnight ferry to Piraeus in the evening.