It is helpful to hear that you can travel without API, which is what I was concerned about. Yes, I imagine that the new passports will do the trick.
I'm flying Thomas Cook to Kalamata this summer (as well as Plakias - lucky me!), and have discovered that doesn't require API either, so it looks as if API is being phased out at least to some countries, but some companies haven't caught up yet.
It still leaves me wondering why you need API if you book extras on Thomas Cook on an Olympic holiday, but not if you don't! Probably a quirk of Thomas Cook's very quirky website.