For everyone else like me (who knows nothing about this radio), some good background info is on
this page, along with some very good
service data.
I don't know much about repairing radios. You might get more precise info on the
Antique Radio Forum.
One thing I have found out from the ARForum, you want to assume ALL paper caps are bad. They very likely are, or will be soon.
I'd suggest you pull all tubes except the 5Y4 (rectifier), the 6K5 (driver) and the 6F6's (push-pull output tubes). You want to solve the squealing with just these in place, before tackling the radio frequency (RF), intermediate frequency (IF) and automatic volume control (AVC) sections.
You may want to lift the end of the 0.01uF cap (part 36), and the end which connects to the 330k (part 33) and 51k (part 31) resistors. This will disconnect the audio section from the rest of the radio. There is a 0.05uF cap (part 50) which runs from one 6F6 plate to a 1M resistor (part 49) and a 0.03uF cap (part 47) which may be mounted on the tone control switch itself. They form a feedback loop-based tone circuit. Killing the loop stops the tone circuit from working, but also may help diagnose your feedback problem.
The push-pull output doesn't have a true "phase splitter" but rather uses a driver tube (6K5) and a self-split scheme to create the push-pull output. Pay particular attention to resistors 62 (25 ohm), 63 (152 ohm) and cap 64 (10uF). They form a "back-bias" circuit for the output tubes, and you want to be certain they're reading roughly correct. Be sure you connect the PT center-tap back to the top of the 10uF cap and NOT to ground anywhere; this too is an element of the back-bias arrangement, and not what you typically find in a guitar amp.
If you can follow this, and be certain everything in the audio output stage is functioning, opening the tone circuit feedback loop may kill your oscillation (or not). Let's start with verifying this section.
Oh yeah... Caps 58 and 59 (both 0.003uF) from the 6F6 plates to ground may be tone-shaping, or may be a form of phase correction of the OT (I don't know enough to know which is the case; PRR can probably tell us). Either way, I'd probably make sure both those caps were replaced with brand new stuff. A leaky or otherwise malfunctioning cap in these spots will either do bad things to the power supply or possibly contribute to a squeal problem.