How do I plan a big shoot with many moving parts?

You can plan a shoot. What overwhelms you is scale, the productions where the moving parts multiply until you cannot hold them all in your head at once. That feeling is not a limit on your ability. It is a signal that you have outgrown planning by memory. Big productions are not planned by holding everything in mind. They are planned by getting it out of your head and onto paper, then breaking one huge thing into many small, ordered ones. No one juggles it all at once. They build a structure that does the holding for them. So for the next complex shoot, do not try to see the whole thing at once. Write it all down, then split it into pieces small enough to handle one at a time, in order. The overwhelm comes from carrying it in your mind. Set it down, break it up, and it becomes a list instead of a mountain.