...But a light tap on a couple woofers produces an obviously bad sound, what research is indicating might be voice coil scrape.
If your speakers are damaged, you're wasting time and money monkeying with the other components. A damaged woofer is going to sound nasty no matter what you do.
It also sounds like you frequently listen at high volume. The ADS, even though an efficient speaker, is a 4 ohm unit and this can be difficult for many amps, but that really shouldn't be an issue for your Adcom. That leads back to a suspicion of speaker damage. Get your speakers checked.