"Dear ex-Homely, I am glad you want to see littleHomely more often and are considering what is best for her. Please send me your suggested schedule for days, times, drop off and pick ups. I am happy to make arrangements by email, including how we phase in whatever schedule we finally agree so that littleHomely finds it as easy as possible."
A bully gets kicks from the victim's emotional distress. If you don't react emotionally to the cage rattling, he'll get bored and do something else instead.
The email I suggest will probably scare the shit out of him. It shows you are no longer a gibbering wreck (well it will look that way to him anyway). It also shows that he will have to do most of the work himself if he wants to continue down the contact path.
The courts only consider what is in the best interests of the child. I doubt they'd think taking DD out of nursery (would he take the day off work?) to introduce 50/50 care after months of 100/0 care would be in her best interests, even if he says you are a big meany to him.
I wouldn't engage at all in refuting lies. Just stick to very simple unemotional practical emails that are all about what is best for DD. Never point out his problems or offer solutions, e.g. 40 minute drive. Just "please send me your proposals by email" "DD is in nursery on Tuesdays, it would not be in her best interests to change that arrangement at this point, please suggest an alternative."