Which "Sunn"??
The big Sunns were big Dynacos, except where Dyna ran 450V-475v Sunn pushed 520V-540V to force 20% more power. Difference between stay-at-home leisure amp and go-out working amp.
To get clean 525VDC without absurd cap costs, some Sunns deviated from a simple big first filter cap charging to nearly the peak AC voltage. Instead they have a small first-cap, a small(ish) choke, and a small second cap. The ripple on the second cap is quite acceptable. The ripple on the first cap is astonishingly large. The choke averages that. The DC is significantly lower than peak AC. But un-loaded, the ripple vanishes, the average DC gets very close to peak AC. Much higher than the loaded voltage.
600V un-loaded does not seem wrong. You do have to buy caps for that cold-start 600V surge. Two 350V in series, minimum. Or considering that these pioneering amps turned out to have lasting value, it might be time to break the bank and find 600V oil-caps which will last a lifetime not mere decades.
I've just simulated a Sunn Model T, a four-6550 amp supposed to idle at +519VDC and roar at +481VDC, and probably pulling over 500mA at roar.
First: go with what you know. When caps are cheap, use one uFd per mA, or maybe half that. A lot of 80mA 2-6V6 amps use 40uFd. So a simple one-cap supply should use 250uFd-500uFd at Sunn T power demand. That's brutal, we see why Sunn looked at other ideas.
Sunn T uses a mere 20uFd for the first-cap. Less than 1/10th the "required" size. They get 150V pp ripple, yowsa!
But after some choke and another 20uFd, it is 13V pp ripple, 2.5%, clean-enuff for pentode mode.
To get 525VDC at reasonable idle, 480V at full roar, I had to use 420V AC (each side). Close to your 800V AC reading. Maybe Sunn's chokes are better than I simmed.
When I try for "no load" (3mA; any less confuses the CPU), I get 587V DC, in sight of your >600VDC observation.
> it's blown fuses if powered up too fast since I've owned it.
In simulation, current can be quite high. This is a design angle which is too-too-tedious to do by hand, easy on PC, so it may have been mis-judged long ago. What model "Sunn", and what size fuse?