If I were going to form a fraternal order, I wouldn't stop with the Temple of Solomon and Knights Templar and Ancient Eastern Shrines.

Instead, I'd go straight for the gusto, e.g.:

"Exalted Order of the Noble Sons and Daughters of the Ineffable Sanctuary of the Most Antique Empire of Atlantis (Lemurian Rite)."

You can't do these things halfway!