Good for you on NO screen time, wish I could say I was the same, we do offer about an hour in the am transition time and an ocassional movie. I'm a pushover!!!
for quiet time? he is old enough to understand, "I need you to stay on your mat!" If he can't handle taking one or two books and laying still while looking at them quietly, or can't stay quiet all together? I would look right at him and say "you are not big enough to listen, so you are not big enough to stay up. I need you to put all your books back and role over (facing away from all others) and go to sleep" I would sit right there next to him for the first day or two until he fell asleep and after that he should get in habit of doing it on his own. Sounds to n\me like he was just "pushing" as far as you'd let him. No ups and downs to the bookshelf, pick a few books and lay quiet or go to bed like a little baby.