When I was learning Serbo-Croat I played Diplomacy online with a group of native speakers and it was very helpful in helping me learn.
Unfortunately I have yet to find a group of Ancient Greek native speaker diplomacy players.
However, playing with a group of fellow learners might well be just as effective.
Diplomacy would be ideal as it has simple rules but negotiation with other players is crucial. Hence if we did all our negotiation in Ancient Greek we should get a fair bit of practice.