Suggested upgrade paths

I am not familiar with these speakers, and I am sure they are part of the problem. However, there is a good chance that updating the amplification, in particular the preamp, will remove what might be distortion/noise at higher volumes, and give you  improved bass definition. I went through this with my NAD integrated, which luckily allowed me to bypass the pre, and try an outboard pre. It made a big difference. 

For $4200 you can have Totem Twin Bison Towers. 
I love them. They will play anything and deliver a soundstage such you hear music not the speakers, they disappear. Best value out there for a premium speaker 

You've posted under "what's playing on your turntable".  Do you have the same issues with bass and sibilance with vinyl? 

if not mistaken, tweeters on those speakers are not exactly in the center.  Maybe swap left speaker to right, and vice versa, just to see if that makes any difference first.

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.