You could try re-wiring all your circuit-grounds so that they form what's called a Star-Grounding System, basically each ground for each gain-stage gets returned to only one point on the Amp chassis, I'm thinking that the screeching-noise you're getting is in fact caused by the Amp going into self-oscillation, which the Star-Grounding System should cure, also make sure that the amp's HT has a suitably rated Electrolytic Cap or two going to ground to bypass any noise on the HT to ground....
If you're unsure what a Star-Grounding System is, you could try googling it....
Using 1N4007 Silicon Power Rectifier Diodes instead of a 5Y3 Rectifier Tube shouldn't cause any trouble, your amp's HT supply should be a bit stiffer and not sag as much, that's all....

Genius is not all about 99% perspiration, and 1% inspiration - sometimes the solution is staring you right in the face.-Frequencycentral.