When you say you don't want to stack, do you mean you don't want to layer the cake inside at all, or you don't want to do a tiered cake?
Industry standard for a piece of unfilled sheet cake is 2"x2"x2".
If you are set on 2" high single layers, and don't want to use sheet cake pans, 2 16" squares and 1 8" square, cut in half to match the width, gives you 144 servings. If every single person actually ends up eating a piece, those extra 6 servings can easily be made up while cutting.
Personally, I would do 2 12"x12"x4" cakes next to each other, 144 servings, no waste and only one seam.
It's also a lot less surface to cover with fondant than making a 2" high cake will be. (I am assuming you are covering with fondant like the picture).
That also means a 2 foot long cake, instead of 3 feet, which can make a significant difference as far as transporting, carrying and displaying go.