There is plenty of availability. You need to get 120k miles into your United account right now if you are going to pull this off.
Why pay a booking service? I just provided a free booking service in my first post. That's all they do anyway.....
The availability that others mentioned is gone now isn't really gone. It is quite easy to get this flight done.
Now you need to route your flight through LHR, where there is availability on the EWR-LHR flight, and LHR-ATH, ATH-JMK.