Interesting thread! Every Oct. when we visit the island, it was a ritual to have dinner at La Perilla Mission. .
Parrilla Mission is owned by the same people as La Mission and Casa Mission. We used to like Parrilla when it was on 30, but it did go downhill a lot before they closed it. We used to like the odd hots side bar. Get something and then argue about what the heck it was.
Then we would go to Casa Mission get the Parrilla lunch menu. Much better deal than the Casa leather wrapped menu and it had lunch of the day (Comida del día). I understand Parrilla is now operating separately (dos y tres) in a big palapa on the grounds of Casa Mission. Haven't actually tried to eat in the palapa.