OK,
Well this one's a "can of worms" usually and moslty, never fun to solve. I'm going to make some simple assumptions first, like what lassoharp was suggesting. Double check those solder connections.
Then get the right schematic and wiring diagram. You don't have a "d". Gotta be an c. D's used a SS rectifier configuration.
Now, I'm assuming the filter caps are all ok. It's not usually one of the first things I'd look at when seeing that kind of problem BTW. Bad filter caps will more likely cause humming or a lower pitched motorboating sound (when putting in higher value ones) and not really a squealing sound.
Even with that said, ater a bunch of years, it's probably good to just swap out all the electrolytic caps in the amp anyway. Especially if the amp sits idle for longer periods of time in between uses. HV electrolytic caps just can't "reform" as well after they're more than 5-10 years old. And electrolytics in general dry out. Even mult-section cans.
Next, make sure the tubes are OK. The 6C10's that are still out there are, well, not so great. And you are subbing for a 6BK11 right (only have the "d" variant schemo here and can't remember)... And you don't have a "d" if you have a rectifier tube. Gotta be a, b, or c.
Then, I'm also assuiming lead dress (wire routing) on the inside was kept the same. Just like PRR said, it's not exactly too stable in there to begin with. You can also get just that kind of oscillation when you get the OT secondary leads too close to the input of the PI. To see this, you can move the OT secondary wires around with a wooden chopstick or some other non-metalic instrument. Or any other signal wires in there for that matter. Great tool for finding those problems when it's "crosstalk" that's making that happen. And they conveniently help keep you from being the "nearest path from HV to ground"...
But, if it's EXACTLY as it was, well then.. You guys are going to think I'm nuts but... Try an output tranny other than one from MM. You can easily see this one. Remove the negative feedback wire (OT Secondary to 6.8K in the D schemo you have). If the amp stops oscillating under the conditions you're describing, try it with someone elses iron.
I'm saying this last one because I've had rock stable designs here start squealing all over the place (but stable at idle), when using their output iron. And I have scope porn along with a well documented test scenario to prove it too. We stopped using them entirely because of that and other little things that you just should never see when purchasing "premium" iron.
Hope that helps a bit!