I have made Randy's American pizza dough and variations of it several times so I have a general idea as to the methodology and logic involved.
Starting with the yeast, Randy's recipe calls for using the SAF Active Dry Perfect Rise yeast or the SAF Gourmet Perfect Rise yeast. If you look at the instructions on the back of the SAF yeast packets, you will see that they both call for mixing the yeast with half of the flour and other dry ingredients. I think Randy was only following those instructions. If that's the case, it follows that the rest of the flour mixture has to be added later. Doing it slowly will indeed improve the hydration of the flour. If you were using another brand of yeast, the instructions might call for proofing the yeast in water before combining with other ingredients.
It makes sense to put the honey and sugar in with the warm water. Both Randy and the yeast packet instructions recommend 120-130 degrees F water. The honey and sugar will obviously dissolve faster and better in the warm water. You don't want to add something like honey to the dry ingredients because it will only pill up and clump. I believe on some occasions Randy puts the oil in with the water also, and on other occasions kneads it into the dough in a separate step. I usually do the latter, because I believe that the flour will hydrate better and more effectively if oil isn't interfering with the process by creating a barrier between the water and the flour. Some people either do not know this, or they don't believe this, or they are just too lazy and don't care and will just combine all the liquids together. I can only speak for myself, but my personal practice is not to combine sugar (or honey) with the yeast in water. I also don't add the salt along with the yeast in water. I either dissolve the salt and sugar in the water (without the yeast) or add them dry to the rest of the dry ingredients, even the dry yeast. As indicated above, I knead in the oil separately. This is classic Tom Lehmann stuff. If you'd like his logic, let me know and I will do my best to explain it.
As far as the dough management and protocol is concerned, I believe Randy lets the dough rise on the counter rather than on the screen. That is, the dough is shaped into a skin, placed on the pizza screen, dressed, and then put into the oven. I don't believe he uses the approach of letting the dough rise on the screen (or pan). I personally don't use the latter approach for fear that the dough will stick to the screen and be difficult to dislodge after baking. It is, however, a common approach, and is frequently used with deep-dish doughs that are allowed to rise from a half-hour to 2 hours before dressing and baking. The process is sometimes referred to as "proofing" the dough. It's purpose is to create a lighter crust.