Thank you for your response (though I note that my own question remains unanswered). Your questions are food for thought, and I am slowly digesting them.
My listening/movie room is small (abt 17' X 11' X 8'), and has nothing on any wall surfaces...until I recently tamed a slap echo by putting up a 52" X 88" panel filled with Rockwool, on the back wall. The room generally is still pretty live.
I think scattering some midrange might be worth trying; it costs almost nothing, and the half-cylinders can be placed almost anywhere. I have no training in acoustics and am not in a position to hire professional help. I am also considering putting curtains across the front wall (behind and between the L &R tower speakers). I am not a fan of the concept of trying to imitate an anechoic chamber although that idea seems to have a lot of adherents in audiophile circles. So what to do? Listen, try things, listen some more....or do nothing?