I have some KA bread flour, so I went back into my kitchen and weighed some of it on my digital scale after scooping it out of the bag the way you do. Shaking the measuring cup as you do, or tamping it to get the flour to settle in the measuring cup, increases the weight of your "one cup" of flour. Using your technique, I got a hydration percent of a bit over 62% (9.8 oz. of water divided by 15.75 oz. of KA bread flour). That's a good number.
You had me worried for a while on the mixer speed, since a total of 15-20 minutes of mixing on anything other than the stir/1 speed would be too much in my opinion. This is another one of those examples where time measurements can be deceptive and misleading. If, for example, you mixed your dough for 15-20 minutes on speed 3, it would almost destroy the dough through overkneading and overdevelopment of the gluten. But 15-20 minutes at stir/1 speed should be fine. Also, the dough will not become overheated even with the longer knead time.
As for the use of salt in relation to autolyse, when I use the autolyse method I add the salt in the last minute or two of kneading. If you'd like, you can dissolve the salt in a small amount of water to allow it to more fully incorporate into the dough. BTW, I am not opposed to putting the salt in at the very beginning of making the dough (where no autolyse is to be used). Salt is hygroscopic (it absorbs water), so dissolving it in the water ensures that it is fully hydrated and won't try to draw water out of the yeast (through cell wall osmosis) and degrade the yeast's performance (even though modern yeasts behave much better in this regard than they used to). Adding the salt in at the beginning also serves to reduce oxidation of the dough and preserve components of the flour, such as carotenoids, that contribute to flavor and color in the finished crust. If you use salt in the context of an autolyse as discussed above, the kneading time should be reduced, resulting in reduced oxidation also. So, either way, you should be OK.
I think you are doing the right thing learning how to tell when something is just right by feel, whether it is Papa John's pizza sauce, dough or anything else. While I try to do the same thing, I tend to take a more precise approach to things because I think it helps me, and others, to get a more consistent, reproducible product. I find that it also helps me to diagnose problems that I or others are having when we have been following precise steps, ingredient quantities, etc. Otherwise, I would be trying to guess where and why something went wrong. That is one of the reasons I prepare such detailed and meticulous instructions for all my recipes. I want people using the recipes to succeed right out of the block and not to have to guess at anything because I didn't fill in all of the blanks. If they deviate, but can tell me how they deviated, we have a better chance of finding out what went wrong and how to fix it.
I hope you keep on working to perfect the PJ pizza sauce. It should complement your pizza dough very well.