You might have better luck if you’re willing to connect in Europe somewhere and/or be flexible on operating carrier.

I would guess that traveling out of ORD you will have a pretty good chance of finding something for around 80-90k each way (160-180k round trip) between now and September.

To get from ORD-ATH on star alliance carriers you have the option of transits in LHR, FRA, MUC, ZRH, GVA, VIE, BRU. I’m sure I’m missing a couple. OP is definitely traveling at a difficult time to find award space but if you keep monitoring it or set some alerts I’m sure you’ll find something.