How do I manage a lot of moving parts at once?

You can do your own piece well. What overwhelms you is holding all the pieces at once, watching them move and change while you try to keep them straight in your head. That is a different job from doing the work, and your head is the wrong place to do it. No one can hold that many moving things in memory. The people who seem to are not remembering; they are tracking. A live, complex thing is not managed by will or worry. It is managed by getting it out of your mind and onto something you can see. When it lives only in your head, every part feels urgent and everything competes for attention at once. When it lives on paper, or a board, or a list, you can see what actually needs you now and what can wait. So stop trying to hold it all. Write down every moving part in one place where you can see them together, then mark the one or two that need you right now. Everything else stays on the list, not in your chest. You are not meant to carry the whole machine at once. You are meant to see it clearly and tend the part that is moving.