As this is the best dough on the board without using a starter, and I just made a batch of 3 balls Friday for later in the week, thought I'd chime in.
1. At least try and get King Arthur's unbleached bread flour, light blue bag. Readily available in most grocers.
2. Lose the bread machine, get a big metal bowl and follow rest below. My mixer broke after I had it for a few months, I don't miss it a bit, my pizza is better now that I'm back to hand kneading. (more air in dough, more bubbles once stretched, lighter texture, better rise)
3. 3 15'' pies uses 660 total grams of flour, make 3 at a time. Each ball in the end will be about 350grams. 1 secret to this pie is the smaller ball size, if it's not meant to be a 500 gram ball, F's up fermentation.
Prep: Mix salt in room temp water with a whisk till dissolved. Add half the flour and all yeast, whisk til smooth. Add most of remaining flour, keep small handful for board. Use big metal spoon, then floured hands in bowl to incorporate. Remove to board, hand knead in stretch and fold quarter turns. Knead about 5 mins, then clean said bowl, oil it, put mass in it for 2 hrs covered. 2 hours later its smooth, knead another 2-3 mins, then split to 350 g balls, knead each one and form balls. Oil 3 Tupperware containers, olive oil as well. Oil BALLS themselves, sides and top, not bottom as oiled container covers it. Poke 3-4 pinholes in top of each lid for gas release, place balls in, sleep for 5-7 days.
To answer some q's you had degassing is if it rises up to lid before you want to make it. Usually this will happen if the 2 hr period before sleep was spent in too hot a place. Just take ball out, smack it down gently to degas, put back in. No kneading, you got it right. Also I think its fine at 5 days, better at 7, wickedly hard to handle but fantastic at 9!
Good luck, hope this helps.
UPDATE: Oh, and 1 more thing is when you take them out to rest before cooking leave them in the containers covered for 1-2 hrs, then take out to board, dust with flour, and cover in saran wrap until ready to cook, last 30 mins or so. You'll get no skin in containers, and I think it comes out better than right to board and covered.
On fermentation the 1st 2-3 days the balls will slump in containers, looks like going in wrong direction, be not alarmed as it starts to go up thereafter.