My system is getting worse - now what?

First off - find a shop that can look at your 810's for you . If you have damaged voice coils this is the equivalent to driving a car with a failed suspension - nothings going to work right.I've heard your speakers and liked them then (20+ years ago) -sold and serviced a lot Hafler 500's over the years.Really suspicious of the frequent thermal shut downs. To be blunt about it - do you listen at head banging volume levels -very,very high volume levels while completely ignoring clipping/dynamic compression? The only reason I think you might not is that I would have expected you to have blown up you 810's by now (probably a few times?).
What sources are you using? Much as I love vinyl - you can suck an enormous amount of power out of you amps trying to reproduce subsonic trash from a non-synergistic arm/cartridge/table/suspension(platform) combination.Take the grill covers off you speakers and observe the woofers while playing at a comfortable volume level.You will see some woofer pumping on most analog systems - but if it is very violent - this could explain a number of things. First - high amounts of subsonic trash are tremendously burdening your amplifier - it's the equivalent of driving around with 30 cement blocks in the back seat. Secondly -your woofers are going to be operating outside their "comfort" range mechanically a great deal of the time - this will massively increase distortion which will be very audible in the lower part of the voice range which is being reproduced by the woofers in the 810.

...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.

Thanks all.

Can anyone recommend someone in the Boston area who can look at my ADS 810's? I figure I'm in the best location given where they were built.

Check with Tweeter, etc. They used to be a big ADS dealer. Maybe somebody still has some contacts. About a dozen years ago I blew out a pair of woofers in my 1987-era ADS 1090s (one generation after the 810), and my local repair shop (in Seattle) was able to replace them with OEM woofers. There are probably some companies around that specialize in rebuilding drivers for spares.

I believe Tweeters has gone out of business. I know the one in my town closed down about the same time Circuit City did.