As Americans I believe that you will have problems obtaining a residency permit for Greece. Residency permits for EU citizens are easy to obtain. And if you had a work related reason to emigrate, that would make things simpler. But I know of no EU country where retirement permits are granted. If I am wrong, I would be pleased if someone would correct me. I would be interested to learn about it.

Alternatively, since you do not plan to live in Greece permanently, your best bet may be to stay for 3 months per year. As Americans you can do that with no visa concerns at all.