Thankfully in the end, it turns out to be a UI design problem.
Take a look at the “Add New Network” screen.
See the first text box with “Enter network title here” in it?
That doesn’t look like a text entry box…
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It’s bigger than all the other text entry boxes on the page.
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It doesn’t have a Description outside the text box itself, the others do.
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The text box frame is the same width and style as the two boxes below it.
It’s a text box masquerading as a heading!
And if you don’t recognise it as a text box and don’t put anything in it, you get “Network not created”. I hate to think how many people this has happened to who have tried and tried, then given up on the plugin – I was searching for another option before I finally stumbled on what the problem was!