This will be really tight with what you plan to do with your luggage. A 55 minute connection is perfectly doable if you're just getting off one flight (via bus) onto another, but collecting your bags alone will eat up most of this time. Things may have changed since I last used the luggage storage at Athens but it is (well, was) right at the far end of the terminal by the international "A Gate" arrivals. Even walking there and back would take 10 minutes. Then you might have to queue to actually drop your bags... Are you travelling in high season? I've regularly made 45 minute domestic connections at ATH but only in winter and never with the bag-shenanigans you're attempting.

The only way I can see this working is if one of you goes to deal with the bags while somebody else goes to the gate, explains what is happening and assures the agents that the other person will arrive VERY soon to board. Of course, there's always a chance that the second flight will be slightly delayed, which would be nice.

Personally, this would totally stress me out and, with only a 2.5hr wait for the later flight I'd take that option and chill in the lounge for a while. Actually... I'd pay good money to spend 2.5 hours LESS time on Mykonos, but that's another discussion.