I'd take the redeye and then the first available flight to ATH.

The most valuable thing J to Europe buys is time. Work a full day, have dinner (and, if no arrival/transit lounge, a shower) in the lounge and sleep after takeoff until descent. Hit the ground running the next day.

It's a little trickier due to points availability in your case, but shoot for the earliest ATH flight you can get and shower during your transit. You'll waste minimal time and get yourself an extra day or two of vacation (but may sleep a little early the first night). Wake up with no jetlag and enjoy your second day in Athens instead of your first.