Thanks everyone for your suggestions.
I've now tried a somewhat more potent PAL source (Panasonic AG-7650 professional VCR), and managed to get the colours a lot more accurate, so it certainly seems that Chris is right on spot: It could be the PAL decoder just being too demanding on the PAL encoding quality of the source.
Here's a screenshot directly from Youtube:
and here's the VCR playing the same scene, as good as I could adjust it on the Sony:
.
I guess it would have been more useful to have a proper test image available on video tape (or even better, a PM5544 generator), but unfortunately I don't.
Colour tones are by no means perfect, but at least it's possible to get the "base" colours right, whereas when I ran the test image from Youtube via the HDMI->CVBS->RF chain (my first post above), the base colours seemed mutually swapped with each other, and were way beyond any adjustability range.
I will also test it in black and white, but that will need to be done using the conversion chain above since I have no other test pattern available, so I would guess the PAL colour coding of the end result anyhow can't be expected to be correct?
So, assuming that the TV actually works after all, if only the source is right, the next question is how to make it accept a less perfect signal, such as the composite video signal of a HDMI converter.
Perhaps it could slightly improve signal quality, and eliminate two potential sources of error, if I skipped the RF modulation and demodulation steps, and fed the composite video directly to to the right place on the TV tuner board. Would that be possible, and do you think it could improve my chances? Also my RF modulators are cheap Chinese stuff.