I'm not sure if we're talking about the same thing. In your thread I think you were cooking the pizza in the waffle iron whereas mine was just a reheat of leftover pizza. The pizza we used was a thicker crust pizza leftover from Old Chicago. We cut each piece in half and then stacked them so that the crust was to the outside for both top and bottom. It was probably about 1.5" thick at that point. When we put it in the waffle iron, I weighted down the lid with a 12" cast iron skillet. Since it was a thicker, softer crust, I think the pattern became much more pronounced.
I also tried it with some of my homemade pizza which has a much thinner crust and the "waffle pattern" was not near as pronounced. There is a difference to the palate since the toppings are to the inside and don't hit the tongue for a few chews. Maybe more like a calzone.
We're also thinking of using our waffle iron like a "panini" press this summer for making tomato/mozzarella/basil panini sandwiches.