...But completely re-doing the Amp unless you are a tech and can do it yourself is just not worth the money for hundreds (which I do not believe the cost will be).
All I can say is, try it and see for yourself

There are plenty of people here who have had such amplifiers re-built, I will let them testify as to how good they can really be, because after that number of years you are not listening to what the designers had in mind.
Even so, if you are looking at the market value, if you do not intend to keep it, then it's not worth it. That being said, prices have gone WAY up in the last 10 years or so that I've been loosely keeping track, more than a good rebuild job included. And, it's not that the gear is not worth the money performance-wise when restored, it's actually that the prices of non-restored gear are excessively high IMHO. You were lucky to get a good instance of an AU-919, but you could just as well have, and for the same price, gotten one that would have worked a month.
From a tech point of view, it's not the easiest to work on and there is a lot to go through. In my own case I have been known to give 30% discount just for theunit being clean and from a non-smoking environment. That sort of crud can do a lot of damage and then you need to literally tear the amp down to the last screw and wash it - including screws! - and you should see what the washing solution looks like after the parts have been washed in it.
Also, prices in Europe are higher for parts but since I am in Central EU labor is cheaper. Try finding a good tech in the US who will work for $7 an hour on a TOTL component and actually knows what the heck he's doing! Which BTW is for me another discount: if I get a blown amp that 'could not be fixed' I'm usually looking at at least 10 hours of 'undo' of the previous 'tech' (or sorry excuse for: if you didn't know what you were getting into you should have staid away from it!). Believe me, I could tell some stories here...
Regarding the question about black flag caps - not all of them will cause the amp to fail instantly but there are some that will. Some are in the phono section and will not cause visible problems unless you switch the source to phono. But for a select few, one intermittent failure is enough, and there are IIRC 6 in the power amp section alone that are dangerous.