The lights dim? Wow... That
can't be good for gear.
You have one obvious problem, and one that may or may not be a problem....the AC power brownouts, and the amp that seems to be overly sensitive.
Regarding the first...
Is the building wiring OK? If its all coming from somewhere else (i.e., you know your wiring is OK), then your choices are pretty slim and all expensive. You need a UPS (uninterruptable power supply) for your gear. A unit which simply protects the gear by shutting everything down (like the Panamax 1500 or the newer 5000 series and Monster power stuff) won't do the job, as they will simply be turning the gear on and off. Seems you need something that will provide power during the brownouts, and a UPS big enough for stereo gear isn't cheap. Something like the Back-UPS RS 1500VA would be a minimum, and a 2000VA would be better. The advantage of the bigger ones would be that you could protect your computer also. Before I went this route, I'd call APC and tell them what I had in mind. The output of these should be a nice clean 60Hz sine wave, but I'd want to confirm that since these are designed for computers and servers rather than stereo gear.
The Sony...
I suspect a problem in the relay circuitry. There usually is at least one cap in this circuit that is designed to discharge very quickly on power down to disengage the relay and prevent turn off thumps. Thie cap is generally connected to the transformer output via a single diode and a low value resistor, and it takes a heavy beating in normal use. It is probably weak.
My only real gripe with vintage Sony gear is related to the size of the company. Sony actually owned their own semiconductor fabs back then (perhaps they still do) and of course many rare and nearly irreplaceable transistors went into their equipment. Your 5550 is one of those. The VFets on the output are uber-rare, and if damaged or destroyed your probably have a paperweight on your hands.
If it were
my amp, I'd restore it just to protect the output devices. Repair the relay with whatever it requires, and replace
all the electrolytic capacitors with nice tough new Panasonic FC caps. The big expensive power supply caps can probably remain as long as the rail volages look OK and the amp is capable or reaching its rated output power, but I'd put a good film cap bypass cap on them to compensate for the increased ESR due to age.
Servicemanuals.net has a
manual for that unit...one of the few places that actually has it.
No magic to measuring the offset. Get a decent voltmeter, set to read DC voltage on a low scale, and connect to the amp output. You should see something under 100mV...the lower the better. Read
here for more details.
I'm in Lee's Summit, MO, a surburb of Kansas City. If you were interested in pursuing this, by all means shoot me an email...you can do so through my profile.