Use the summer to trial some party games and see which ones are the most enjoyed? I'd mention some, but other than Werewolf, I can't really remember any (Never really had many friends growing up, so never got to experience a lot of the good ones), so I'll leave it to people who actually know more.
However, if we're looking for some minigames that might be possible... Theoretically, modifying Hide and Seek to pass the Seeker on to the first person found without a hide time could make for a game of Tag. It'd be a time-limited game, but maybe the way to win is to be tagged the least amount of times?
I don't think we'd be able to wrangle enough players together for a game of chess, at least not the way I was thinking of playing it. Two people in control of the chessboard would be easy enough. It would be the 8 pawns, 2 rooks, 2 knights, 2 bishops, the queen, and the king on each side that would be nearly impossible. I don't think, even at the best, we'd get 34 people interested in a chess game, even if it was promised that people were playing as the pieces.
Much as I'm not one to suggest something I can't do, have a major summer build competition, like Build Battles but on a larger scale? Potentially with two, or three, people working together on a summer-themed plot, if there's enough interest.
I know this would be more of a tour and less an event, but maybe it helps someone kick an idea over. "The Journey Home." We have the Fellowship Path leading us to Minas Tirith and Osgiliath, plus a bit further, and I found some footprints outside Minas Morgul, but I wonder at what point we could start following the Hobbits' journey back home to the Shire, as best as the Loremasters of the server can pull that together.