Jackie_W you are a genius! Yes, ticking that setting on docx input fixes it; on top of fixing the problem, you also worked out what the cause was (which makes sense in hindsight - for example, if I didn't bother adding a cover in one of the tests, Calibre chose the logo as a cover, and if it wasn't there it created a random design with the title on - probably because of the behaviour you spotted). It also explains why some of my tests worked e.g. with other images - they were probably just lower resolution, rather than it being anything to do with a dodgy png.
This is great. I'll lower the resolution of the logo (a hangover from the 300dpi requirements for the print copy) and also add to my notes to tick that option.
In a way it is funny that over the last few days I have done about a hundred conversions, installed several new bits of software (none of which worked), and edited stacks of trial images - and the answer all along was a tick box! I generally avoid ticking things I don't understand, probably with good reason, and keep settings as close to the default as possible, but that's one I should have known about.
I can't thank you enough. If you want (correctly-formatted) epubs of any of my books you are welcome!
http://www.karldrinkwater.uk/