Interesting, Peter. I most often have that "shaggy" dough ball look as Tom describes after mixing/kneading for a very short time, like 60 seconds. But I start first mixing all the dry ingredients in the bowl first, then the water and water with the proofed ADY, then the oil, etc. and, of course, mix by hand. I don't necessarily understand the importance of the sequence of putting the ingredients together, but I'll have to try Tom's suggestion and see the results. While it sounds like it was intended for thin crust pizzas, I think the methodology has definite application for deep dish style also. After the first rise with one of mine, the shaggy look kind of disappears and esp. after then putting it into a zip lock bag and into the refrigerator for a day or two.
In Tom's description, he talks of adding just half of the flour at one point, then salt and sugar, then the remainder of the flour. While he didn't mention it, I wonder if he meant to wait a while and do a kind of autolyse. Am always looking for some new good ideas.
The PMQ thread discussion you referenced was interesting, too. Altho I didn't follow the gum line issue too closely, several pizza owners described their similar processes and the owner of a pizzeria in Missouri, just southeast of KC, indicated a similar process. Their website showed a Chicago deep dish pizza (pictured below) and I imagine that they might have followed a similar procedure for it. The texture of the crust on the pizza looked very good.
An interesting aside regarding the Missouri pizzeria, which is called Next Door Pizza, is the description on the site how they got started: "The recipes themselves are completely original and are the result of (the owner's) cooking over 700 pizzas in his home during the past year. Daily, (the owner) himself makes all of the dough in-house."
Can you imagine making over 700 pizzas at home during one year?