I guess there are no experts left for this area. :-)
The cause was not obvious, but UAC settings definitely had an effect. As I said in the original post, VB6.EXE was running as Administrator, but it was also running in XP compatibility mode (forgot to say that) which is an acknowledged requirement.
Setting my UAC level to the bottom (Never Notify) and rebooting the machine made the IDE error disappear, although it had still occurred (quietly) because the relevant classes of the control (e.g. DTPicker) were inaccessible and it wouldn't compile. Oddly, though, restarting the IDE made it work.
I couldn't believe this as I had made no changes in between. I pushed my UAC level back up a notch and rebooted. The error came back, so I lowered it back to the bottom setting and everything seemed to work OK the next time.
I don't understand this. If anyone else tries to follow my sequencing then don't be alarmed if you find occasionally that the IDE won't uncheck mscomct2.ocx from the Control list because it is "in use". The symptoms seemed to vary as I made these changes, and when I tried to reproduce things to publish a write-up here, nothing seemed to behave as it did the first time.
I am now running with UAC at its lowest level and mscomct2.ocx loads OK in the IDE. As far as I can see, this was the only control that was experiencing this issue -- the code uses quite a few others and they were loaded OK by the IDE.
I hope someone else finds this valuable. Without an explanation, I am still a little concerned