To state the obvious: When left alone I start with the complicated stuff then plow though the remaining easy bits. When disrupted regularly I grow a giant void in the middle of my project where the complicated stuff should have been.

Um, yes.

But managers so enjoy the feeling of having minions at their beck and call - and how can mere reality compete with that?

Try a different hierarchy? I imagine there could be someone at the bottom of the salary scale who only does information gathering, no responsibility, no ability to act on it. You periodically call them in to rubber duck them and/or write them a progress report.