Upvote:2
I do not know precisely how this works in Greece, but my parents have some similar experience in France. the penalty for failing to register should be fairly light, but the specifics are determined by national law, so they vary from one country to another.
I suspect that you can get away with doing "visa runs" (perhaps "free movement runs" is a better term, as odd as it is) if you won't have a regular home base during your time there, and you might even be able to get away with it if you do have a regular home base. But I would counsel you to consider a couple of points:
If I were you, I would probably try to stay above board and make the application to the Greek authorities.