"I don't think that the high frequencies are the problem."
You may not think HF's are the problem but I think you might be mistaken. A funny thing happened to me a while back when I listened to a DIY Class D amp. Initially, the first 5 minutes it sounded all right but certainly not perfect, transparency was amazing but.....after about 15 minutes I started getting a headache. I'm not being sarcastic, this really happened. The problem immediately went away when I replaced the amp. The REAL dilemna was I never could figure out what was causing the headache. The same amp in the owner's system didn't do this.
If you're not listening too loud, which could certainly cause ringing, you most certainly have an issue with the upper frequencies. The cause is less clear but it could include the amp/speaker interface, most likely IMHO. Room treatments and speaker placement may help ameliorate the issue. It's tough to tell without knowing everything. Do you have any audio buddies or a wife that could chime in with their opinion? It might help narrow things down a bit.