Because Monty's choice was not random (he didn't open just any box, he revealed a goat) the remaining probability of two-thirds gets squeezed, as it were, into the third box.
If the name of the meat is just too "Three Billy Goats Gruff" for you, call it "capretto" (Italian for "kid"), like chef Scott Conant does at his five Scarpetta restaurants, where he serves it whenever he can find a good supply of extra-tender, young goat.
If he goes a more traditional route with the meat sandwich, he may get creative with the vegetarian one, trotting out a goat cheese and olive or artichoke-cheese sandwich.