I always knead my deep dish by hand, too--great fun! You should be able to mix a small batch very quickly--if I make a dough based on 1.5 cups flour, for example, I can mix it (just getting the flour and liquids to come together) in about 30 seconds. After that I knead a Giordano's (or Gino's East)-style for exactly 2 minutes--it comes out into a pretty smooth round ball.
For an Uno's/Malnati's style, I would try kneading for even less time, as their crust seems "looser", or even more biscuit-like than Giordano's/Uno's (which tend to taste more pie-like). You can try 1 minute or 1.5 minutes. Also, I would make sure you have enough oil (at least the rato of 3 TBS: 1 cup flour) if you want to duplicate the greasiness of their restaurant taste. Uno's uses soybean oil; Malnati's uses corn oil. if you experiment, you'll hit on it!