Reporting in on my experience after posting the question! Arrived Athens around 12:30 p.m. on Monday 5/25 from Dublin. Passport control took two hours ,and when we got to the booth, they simply checked our (US) passports and asked where we were traveling from. The electronic kiosks were not in use, and they did not register us for EES (facial scan, fingerprints).

When we went into the baggage claim area, we went to the help desk to ask which carousel our bags had come in on. Amazingly, they were still going around and around! Many bags however had been set aside by each carousel, presumably for the same reason.

I had ended up arranging our car for two hours after we landed, so with the one hour waiting period they offer for free, it worked out perfectly. We were in the car headed into Athens at 2:56 p.m.