Thank you all for your input!
And thank you G Edmonds for the kind offer to assist further!
Since my initial message, I did a more careful reading of the service manual and, lo and behold, it has a very nice troubleshooting section.

I need more patience and probably better glasses too.
Anyway, after following the steps in the "troubleshooting tree" for the power supply, I narrowed down the problem to the separate power supply for U1030 - i.e. mainly Q1021, Q1022 and VR1020.
And the culprit was... the 6.2V Zener diode VR1020 which, funnily enough, was still measuring fine in forward bias and even in reverse bias, this latter one for a testing voltage above 6.2V (i.e. using the 15V range for diode measurement on the 121GW multimeter).
However, testing in reverse bias with a normal testing voltage (i.e. about 3V), the reading on the meter showed something like 1.x - 2.y voltage drop.
So, m k was right in his assessment that Q1022 was turning on too early.
The Zener diode was replaced and the PSU is now working fine.

Ah, and to answer my other question: the service manual also mentions the PSU does require a minimum load to regulate properly, at least for the +5VDC power rail (at least 2.5A, if I understood correctly).
Now, my next issue is related to CH2 which seems to have a problem with the VAR knob:
- Even in its "detent" position, the readout shown on the display includes the ">" sign for the scale of the vertical divisions (that would normally be displayed only when turning the VAR knob out of its "detent" position).
- With the VAR knob in it "detent" position, the amplitude of the signal displayed is 50% smaller than it should.
I should probably DeoxIT all pots, as I suspect the one for CH2-VAR is probably not making good contact in its "detent" position.