So as far as I can tell, there's no sign at all that "radio frequency management" across your home, ie. carefully selecting the "right" channels for each of your wifi Access Points, will make any difference.

This is not to say that choosing channels carefully never makes a difference.  For example, at an office, you have very large rooms, very good signal propagation, and a lot of computers (and APs) in a small space.  If you don't manage your spectrum in that situation, you're screwed.  Enterprise APs do an amazing job at this.

But in your home, it's different.  There are far fewer people.  There are far more walls.  There are neighbours who aren't cooperating anyhow with whatever scheme you choose.  There are only 3 frickin' channels to choose from anyhow, on 2.4 GHz.  (And on 5 GHz, there are so many channels, and so little penetration through walls, that you don't need to be careful.)

In such a setting, I literally don't think you can make any improvement over simply having a decent (non-coordinated) autochannel selection on each access point separately.

Can anyone point to any research that disagrees?