Suggested upgrade paths

Looking at the specs of all your equipment, you should have no issues unless something is defective, even in an 80+dB territory. You should cruise in the 70s with no problems. Your speakers not sure. The amp should be good for 10-20+ years. Rotel is a respectable brand.

This gets me thinking. I brought out my PS Audio Sprout, which is 3 lbs, has Bluetooth,  built-in DAC and headphone output. Price is about $700. Pushed it into the 70s with peaks of 85 dB, and it produced no sound characteristic that you described in your system. While off the wall comparisons, I do not see your equipment being a problem. One could say I can not distinguish the difference between a low resolution and a high one. See my virtual system. The Sprout may be a little squirt, but it puts out some good tunes.  I can not imagine your equipment sounds any less. I'm sure more.

What's the sequence for implementing your system?  What came first and so on? At what point did you experience the sound issue? 

Note: Doing my Sprout testing at high volume has my tennisus loud. Perhaps peaking at 85 dB did the trick.

+1 on the Totems.   I like mine!

I have a pair of Super Lintons driven my Marantz KI Ruby CD/Integrated.  In my system I do not find these shrill or edgy at all.  I find them to be a great speaker that excels in real world systems.  They can be placed a foot or two off the front wall and have deep extended bass without any boom.  They image beautifully. And while the tweeter is revealing, it in no way crosses the line where I feel the need to reduce the volume. Quite the contrary.  Different rooms, different ears, different systems, YMMV.

oh, and assume you’ve played with toe-in (e.g., less and no toe-in)?

I don't think that a sub will help the problem you describe. I am a Harbeth fan at this price point for the quality and balance of the timbers. Owned monitor 30.2 with Ton Trager stands. It was an outstanding combo. The 30.2 is known for its mid-range and voices and the HL5+ are not as good in that range but have better bass and are more forward.it depends on musical presentation taste. You have to look at replacing the Rotel 1592 down the road however IMHO. Good luck and keep us posted.