Thanks again for your suggestions and advice.
Yesterday I did a reasonably successful colour adjustment (using the VCR as source) and managed to obtain a more or less completely B&W picture, which would indicate a healthy picture tube if I've understood it correctly:
However, I got it with the red screw turned almost all the way down. It seems to me that I have a somewhat weak brightness, which I've compensated for by setting the contrast knob at max. I will try the B&W adjustment again, and aim to get a balanced grayscale with all colour adjustment screws at a more generous setting. Based on the assumption that it could at least slightly help up brightness, but perhaps that's wrong.
Anyhow, here's a photo of the colours after the B&W adjustment:
They do seem correct, hue-wise, compared to the Youtube screenshot:
Enter the HDMI converter:
Roughly, red turns green, green turns red, and blue remains blue.
If I disconnect the RF cable, and allow it to just barely touch the RF output connector of the RF modulator, the TV is able to decode the colours correctly:
So there's something in the output signal from the HDMI-> PAL conversion which confuses the colour decoding. I will certainly try your suggestion with VR303, Chris.
It would also be attractive to be able to bypass the RF modulation and demodulation steps. Is there any obvious position on the board where I could hook up a baseband signal?
What to use it for? Well, I guess learning at least something about CRT and analog TV along the way is reason enough. And if the alternative is to use it for nothing, and return it to the dusty corner where it came from...
And with an HDMI input, I could use it for Chromecasting, Rasperry Pi and other modern sources, but with that good CRT-and-wood-cabinet feeling.
One more thing, Chris, with regard to your comment on NTSC: The TV does not respond correctly when I switch the HDMI converter to NTSC either. Please note, though, that this is a KV-1300E. I've read somewhere that Sony for patent reasons implemented their PAL encoding differently in the UK models than in the models aimed for the Nordic market; perhaps that could be an explanation.