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.

Johnny got a good point - your test procedure for woofer failure may not be valid? I'm going to try and describe how to test for a warped woofer voice coil. Let me make one point first : This is something you do to your speakers - YOURS - never ,ever do this to anyone else's . If you do this on someone's sales floor without first asking for permission - anticipate a violent physical assault on your person - which you richly deserve.In my 25 years in the industry I replaced dozens of drivers damaged by f#$%^&g idiots punching in domes or dustcaps on my demo speakers.Industrywide - you will find service people who have a real attitude about this kind of damage.
First off - this test procedure is only useful for woofers and a very few mid-bass/mid-range drivers that have a fair amount of excursion ( front and back motion).Most midranges and all tweeters that I am aware of will not tell you anything about their V/C condition with this test - you will however have a reasonable chance of permanently damaging them by sticking your fingers into them.
All we are trying to do here is feel and listen for a voice coil that is no longer round and/ or no longer intact ( voice coil wires have come loose).Most woofers have a obvious dust cap over the voice coil it's self - this will be at the exact center of the woofer - DO NOT TOUCH THE VOICE COIL CAP-COVER.Use both hands - spread your fingers evenly onto the woofers cone area a 1/2 inch or so outside the dust cap area and GENTLY press down - you want to get the cone to move as much as possible straight back - if you only press on one side of the cone it will probably scape - this doesn't mean anything- then release the pressure and let it spring forward - it should move forward freely and you should hear nothing. You do not need to push the voice coil to the bottom of the V/C cut in the magnet - if you can move it a little bit - you should be able to tell if it's moving freely and if there is no scraping or rubbing sound from the Voice Coil cap area.If it scrapes,catches momentarily or you hear a sorta whispy higher frequency brush sound when you do this - the voice coil is damaged.If it moves freely with no sound - at least the Voice coil is probably not damaged ( this doesn't always hold true - some prosound speakers have really wide gaps and the V/C can burn out and not scrape - not common on consumer stuff).Anyone who services speakers learns how to do this probably within their first week on the job - while not definitive - it does allow you to separate the obviously damaged from the maybe's - always useful in a service job.This will work work for something like 99% of Hi-Fi woofers ( pulp and plastic/poly cones) - a very few designs use Styrofoam like cones materials - very easy to try this and stick your fingers right thru the cone . If you're not sure - don't try this.
Be careful - but this might be of some help in analyzing your problem.