Jay, one additional suggestion that I thought of and if I can make . . . on the edge of the pizza dough in the cutter pan is to follow my "press, pinch and crimp" procedure and do so on the edge of the pizza dough in the pan before baking. This may not sound like much, but I dare others to try it and tell me it doesn't do something good to really help in the total tasting experience of Chicago style thin crust (or even deep dish) pizza eating.
The partial pizza pictured below was from Villa Nova's pizzeria in Chicago, but kind of gets to what I strive for, which is a rough, irregular, "moonscape", pinched appearing edges. May sound screwy, but it is very helpful in the total taste experience (at least the treasured "outside pizza pieces). In any event, suggest to others to at least just try this seemingly minor step and see if it delights and pleases your and your's taste buds more than others.