I can't be certain Hamburguesas El Tío Memo doesn't have any Yucatecan specialties, but I don't recall any and my menu photos (which may well be incomplete) don't include any.
Facebook is one of your best bets - you can find people selling all sorts of things for delivery, including
Lechón al Horno on Saturdays,
Cochinita Pibil on Sundays,and
Frijol con Puerco on Mondays. A good place to start would be the group
Comidas y Postres de Cozumel.
Listed in order of my personal preference:
- Cochinita Pibil: Restaurant Tamarindos on Sunday, Monday, Tuesday, Thursday, and Friday, La Choza on Sundays, El Súper Hit, Ix-Kool
- Frijol con Puerco (on Monday, as is traditional): El Moro, La Choza, El Súper Hit, Ix-Kool
- Huevos Motuleños: Everyplace
- Kibis (Lebanese food is very traditional in the Yucatán): Tacos Arabes
- Lechón al Horno: Restaurant Tamarindos on Wednesday and Saturday, El Súper Hit
- Marguesitas: At the Parque Benito Juárez (the Zócalo) at night, across Av. Xel-Ha from the downtown Chedraui at night
- Panuchos: El Resbalón, Taqueria Molina at the Mercado Municipal
- Papadzules: Casa Denis
- Poc-Chuk: Las Palmas, Asadero El Billy, Casa Denis, El Súper Hit
- Queso Relleno: El Súper Hit
- Relleno Negro: Restaurant Tamarindos, Taqueria Molina at the Mercado Municipal every day,
- Salbutes: El Resbalón, Taqueria Molina at the Mercado Municipal
- Sopa de Lima: Restaurant Tamarindos, Casa Denis, La Choza on Saturdays
- Tacos Arabes (Lebanese food is very traditional in the Yucatán): Arabian Tacos, Los Nopales
- Tikin'Chik: La Candela
- Tuchitos: El Chino Marentes
- Xikil-Pak: Ix-Kool
Queso fundido is great, but not really Yucatecan (it typically uses queso Oaxaca or queso Menonita). I like the queso fundido (especially quesongo or con rajas) at
El Pique.
I would invite anyone to add to this list, keeping any additions to Yucatecan specialties (for example, who has good Lomitos de Vallodolid?) and only dishes you've personally had at a given restaurant.