Possible causes of a loss of TV signal after reorganising masthead amp and splitter
So it turns out that this wasn't a signal or hardware issue, it was an air-gap issue. I'd incorrectly labelled one of the cables and ended up thinking both ends of the same cable were different cables (that's what you get running cables behind walls).

After discovering this and plugging the correct things into the right places, everything worked as expected - except I feel a lot sillier than I did before.