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SOLVED: It's always the way ... spend hours looking for the problem, then post for help and find the answer a short while later. Doh!
For some reason the theme has a favicon.ico and favicon.png, which I changed, but there is also a icon.png file which serves as the favicon! I don't understand why it was done that way ... but that's the solution. Change the icon.png file as well, and it all works perfectly.