I have a little report.
It did not matter if I had only the HQCT connected to USB.
But the different software behaved differently. Maybe you are right that this is because I've got an (untested) HQCT-e module?
The RRHQCT original ver 2.0 - WORKING (I think)
CPCTuner 1.0.41 does not start at all
CPCTuner 1.0.42 (splash says 41...)
CPCTuner 1.0.43 is the same