I am glad you diary here because your sitch provides a good example to others, but I don't comment much because there's not a whole lot I can add. You're doing all the right things.
The board game night sounds excellent. We use to have board game nights (before my H moved out and after, we'd have them without) until D13 started her "teen years". It was 75% good natured fun and 25% bickering, but I would still put up with the 25% to have the 75% back. I am envious.
I was talking to a friend the other day who recently broke up with his GF. He described his relationship as 99% perfect. I think that's the problem - our minds somehow turn our relationships into all bad or all good. Or we recognise the bad in others but take away their responsibility (we internalise their fault, or we make excuses for them). That's what you use to do, you would see his bad behaviour, and make excuses for him (work stress, if I recall correctly). I think that's the biggest change in you. You see him for what he is (good and bad) and you allow him to own both. He IS a good father. He can sometimes be a sh!t human being. I don't think he is trying to manipulate you either. I think he is just trying to do the best he can, and sometimes, because none of use are perfect, he effs up. I think you are now at a point where even if he does *** up, you can look at the intention/motivator, and not the action.
Not wanting to show you his schedule is his own trauma/childish/gut response to a feeling that doing so would be relinquishing control. He processed (consciously or unconsciously) that fear and came out the other side thinking that the request was a reasonable one.