Ok I've determined that if I were to expand the dimensions of a cocktail cab to fit this monitor then it would no long fit through the doorway into my game room. Therefore, I'm just gonna stick a 19" monitor into a cocktail cab and build a classics MAME machine.
I will likely be building the 27" SVGA monitor into a TMNT cab as originally planned. That's a project for a much later day, though. I'll be doing the cocktail MAME cab first. That one will make it up the stairs and into the game very easily.