This company is now basecamp and has managers: https://basecamp.com/handbook/06-orgchart
They also state very clearly themselves that 37signals was "disorganized". https://basecamp.com/handbook/05-product-histories
So... yeah.
Fascinating topic to discuss. Thanks for sharing the work!
The most critical piece of the discussion, to me, centers around the degree to which we can overcome our internal biases in presenting qualitative information. I'm a big fan of Kahneman's book, "Thinking, Fast and Slow", in which he establishes on quite a number of occasions that there is often little we can do to act and think in a manner that is truly unbiased. It is part of who we are as humans.
Generating truly meaningful data, be it qualitative or quantitative, is an extremely effortful exercise. However, I believe that we can overcome the flaws in the generation of quantitative information much more readily than that of qualitative information, which will always be subject to our internal biases, no matter how hard we try to avoid them.
The class of algorithms you're talking about are called job shop scheduling optimization problems.
TaskJuggler http://www.taskjuggler.org/ says it handles this kind of scheduling, but I've never used it extensively.