The Keyboard 'Space event is down' ads some counterforce to soften it all some, when you release the things. It might need some adjustment. Else those things jump everywhere if you push the paddles back.
And yes, 'Space is not down' works against the gravity force. Its just pushing against the falling things. They fall due gravity. Thats was key and a demand in your question. Can rotate those paddles in easyer ways. You wanted it done by physics. And that got me curious. Just like you, i am here to learn by trying to solve other poeples puzzles.
Regarding the big numbers. Its is a bit like in real live, if you only apply torque, you need a lot of force. Try closing a door by pushing close to the hinges.
I did't choose those numbers by logic. I just made them big enough to push against the against the gravity, by try and error. To be honest, i did't gave it that much time.
I just mimicked real life physics.