I wanted to thank everyone who responded to my original query.
Even without Covid, my preference would generally have been a non-stop to ATH ex-US (less hassle, fewer risks of delays, less risk of baggage loss), and with Covid, it certainly was (I'm fully vaccinated, but am among the vulnerable population, so am continuing to try to minimize risk). I'd booked a NS on DL, but was subsequently notified by them that my flight to ATH had been canceled. For my planned travel dates, AA was pricing prohibitively (either as an award or a paid ticket), and UA was using its old, non-Polaris (no matter what they call it) equipment. When I found an award on LH priced at half the miles for the UA flight and showing a 747 to FRA, I grabbed it, but then woke up the next morning worrying about Schengen's impact on the transfer and posted here. (Greece had already announced that it planned to open to vaxed Americans, or I would not have even considered going.) I decided the additional uncertainty over the transfer was not worth it, and was working on changing my travel dates, when I saw that DL had reinstated a NS on my preferred date, and I am now rebooked.
Thank you all again.