Update: (the one where I make progress, I think):
Room/Space Treatment Gurus (you know who you are): I opened up the window coverings on 100% of right wall: ~125 Sq ft. of glass is now reflecting into the room, rather than the textile window coverings that were closed over the wall. The good news: I could hear more highs. The bad news: the difference was quite small--I was reather pleased I could detect it.
Power Conditioner (and anti-so) folks: I have now got the power amp directly in the wall, and the other gear in the power conditioner. There is no longer surge supression on a separate (Monster) power strip. Just one thick gauge power strip running off one socket of the conditioner. The other three conditioner plugs have CDP and Pre Amp and DAC in them. It's a cleaner hookup, and the difference from taking out everything (and running off the wall directly) has persisted, I think.
Near Field People (you are wise, soix et al): I followed the advice of several of you (finally). I stuck my ears at the center of the bass element and then the tweeter on the Hawks, while listening at very moderate, then slightly louder levels to Sultans of swing. Range 1-2" from the plane of the speaker housing (or tweeter dome). I think this is a serious finding: Left tweeter almost nothing coming out, with nothing in the upper-highs, and maybe nothing in the mid-highs. a little low-highs. No distortion at all (I think this is important--I listened very closely). Right Channel: Interesting--I heard the lo-highs, mid-highs, and hi-highs--all of them, but overall the signal was very very attenuated from what I might expect. It was not the case that "if I had both speakers firing like the right one it would be great. The right tweeter was, on an absolute level, was attenuated.
Please comment. Thanks.
I'm thinking, after the amp swap-in, I'll contact the dealer about Hawk service possibilities. I may also try sticking some other, much lesser speakers into the system to test: Axiom M3 v3. I will have a lot more data than.
ghosthouse and others who think it's the speakers: I think we are homing in. Thanks. It could still be the Sim Audio Moon P-5/W-5. Hope not. The speaker swap-in I mentioned above should help.