I don't always respond. I haven't responded to his latest emails. If I do respond, I usually don't respond right away. But if I offer no response whatsoever, he can use that against me in court to argue that I am ignoring his requests to visit, and hence the court should afford him more visitation rights and autonomy.
What I have been doing is offering brief, vague answers, and usually responding with questions. I have to basically take the high road and kill him with kindness, which is what I'm doing. Because then he has no ammunition to claim that I blocked him, or hindered his access, or that I am making decisions based on my personal dislike of him. And then in contrast to my level-headed, accommodating responses, his escalation is all the more obvious and deranged.