My new 8566AB now works nearly flawlessly, only a few PLL unlocks, but that's probably all fixable.
Removed damaged front panel and installed replacement front frame from old 85662A. Since the metallisation beneath the paint of the damaged front panel was flaking off, I decided to strip all that stuff and dumped the panel (plastic only, all metal except the brass screw nuts) into a bucket full of dilute sodium hydroxide solution (prolly about 5-10g/L).
I thought that the metallisation to be aluminium, but it isn't (probably nickel, but not sure). Thereby the process is very slow (aluminium foil is quickly eaten by that solution). But it still gets dissolved somewhat and the metallisation layer can easily be stripped with high pressure water jet cleaner after the panel spent a night in hydroxide solution. No harm to the plastic whatsoever (solvents will probably harm the plastic).
Since I couldn't wait, I borrowed a front panel from other 8566 and installed it. But new 8566 was dead, both red LED were on. So I checked voltage rails (only with Keithley 2015, dumb idea), +5.2V rail was at 4.3V, so there's must be a tantalum cap short somewhere, I thought and started to remove cards. But with all cards removed, both red LEDs were still on and 8566 was still completely dead. So I swapped CPU cards from good unit, but still dead unit.
Then I decided to check voltages again but used trusty Tek 7904A with 7A13 this time. And big surprise, the 4.3V on 5V rail turned out to be more or less 100Hz AC from rectifier, with 4.3V DC content. Which means that this biga** blue 30000uF cap on the 5V rail is completely dried out. Don't let size foul you
.
Put everything back together and borrowed that cap from other 8566 et voila, working 8566.
Now only need to fix that front panel and find out, why those 2 PLLs refuse to lock.