How do I make this particular pizza dough?

Not to disparage some of my go-to cookbooks, but when I want something that's a little more institutional or American traditional (and I'd say your pizza qualifies), the first places I look for recipes are the Better Homes and Gardens Cookbook or the Joy of Cooking. I would bet that their recipes are going to steer you toward that kind of pizza crust.

I would think you'd want to look at a dough recipe with some fat in it--most likely olive oil. And I would think two rises would be good to get that sandwich bread texture of smaller bubbles/tighter crumb. Compared to a traditional Italian pizza, you'll also need a lot more dough, and I expect you'll cook it at a lower temperature than for a thin gourmet pizza (which is usually as hot as your oven can go).

If you're concerned about thick dough coming out a little undercooked (especially in the middle), you could blind bake it (with no toppings) briefly before taking it out and topping it.

If you're feeling really desperate for "that kind" of pizza dough and don't think anything you'll make will be white bread enough, Pillsbury makes a dough in a can that you pop open like their crescent rolls and cinnamon rolls. Pop it, and the dough is inside ready to rock--just unroll it and go.

I know exactly what you are talking about. I've been making pizza for many years, but only recently have tried to replicate this pizza that I grew up on. I have a very strong feeling that the crust was a very generic biscuit dough formula. Once the pizza was cooked, it could be rolled up (school pizza is soooo good that way!) but you had to really take care and roll it slowly or the crust would break. Very different from a regular crust.