According to the Lonely Planet guide there's a bit of a strange situation regarding staying on Meis. Apparently, if you are going to stay on Meis for any length of time, you must arrive on a Greek registered boat.
"What was written below was merely the situation at the time of writing..........You can stay overnight on the island only if you travel on a boat owned by a Greek captain...............You can't stay overnight on the island or travel onwards to Rhodes if you take a Turkish boat."
I don't know whether this is still true, or whether it was a fact, but I'd check it out if I were you. The LP suggests that you phone the Tourist Office in Kas, but doesn't give a number.