Hey thanks everyone for taking the same to direct me to the good sources, things got in the way and I just had time today to implement what
pdf64 was recommending trying, that is, to lift the bypass cap on V3. Unfortunately, by doing that I'm getting more distortion, just as ugly but slightly different, that one does sound like what people describe when they talk of blocking distortion.
So I'm going to do the next thing you good folks recommended that is changing all the bypass caps on all the cathodes. I still have the "Made In Japan" ones so a cap job on those is past due. Let's hope that's what the issue is. It might take some time as I'm waiting on a potential customer's decision on a custom-made pedal and I'm trying to keep supply's shipping costs reasonably low by grouping my orders.
From Merlin's web site, scroll down to > page 25 > 1.18/K bypass cap;
Sometimes the answer is just sitting on my bookshelf, thank you
Willabe for reminding me!

What I wanted to say is that without some fresh bypass caps, it's difficult to know what's going one. Those caps in GA-1050 are easy to get.....Mouser, Digikey, Farnell, RS. As I normally work with HiFi-electronic, I have lots of different ones available. Elna, Nichicon, Phanasonic.....but I'm aware this does not help you :-)
I understand your frustration, but let me explain my approach. I'm not "just" trying to fix my amp, I'm trying to
learn, with your help, how to fix amps.
The context here being, I always play this amp clean, partly because I know it has that weird crying distortion in the back, but also because that's my clean amp, so eventually I sort of forgot about that problem. The recap job brought the tremolo channel back to life and fixed the tremolo, great, I got a little enthusiastic and decided to crank it a little, and there it was still, that ugly distortion.
If, indeed, the problem is the bypass capacitors and I had changed them with the whole cap job, I would not have had the problem anymore but I would also have no clue as to what I did that fixed it and which was the incriminated capacitor. At this point in my journey, the process to get the amp to work is almost more important than having a working amp. A fixed amp is useful to the guitarist that I am, it is utterly useless to the amptech I would like to become if I have no idea how I got it to work.
I understand it's annoying to have yet another thread popping up about problems on the same amp after the last problem got fixed while the symptoms might all be related but I need to understand the cause of each individual symptom.
For all I know, my problem could be too much signal entering a following gain stage, could be the bias of one of the tubes, could be subsonic oscillation, could be an open resistor somewhere. This is my first amp on the bench, some people here have seen thousands, I'm not asking them to fix my amp, I'm asking if they've encountered this problem before, what comes to their mind when they hear those symptoms and what was the thought process to that hypothesis.
So that is my approach. I certainly do not wish to waste anyone's time or patience.
In any case, your help has been precious and I have learned something yet again, about amptech workflow and standard procedure, which is extremely precious to me. So thank you very much, I will report back when I get those last caps changed!