Hi Doctor J!
Thanks for the speedy reply!
So I took your advice on board and gave the neck some slight relief to the point that the strings weren't rattling any more (no rattles anywhere up or down the fret-board, open string or otherwise).
I then intonated the bridge again and did the test of pressing down on the first and last fret and checked the 8th and 9th fret and can confirm I've got the gap to just less than the width of a business card.
So far so good!
However, the action still seems utterly rubbish.
I've attached a photo for reference.
For background, this is the first and only bass I've ever owned. Perhaps I'm being overly finicky about action height based on coming from guitar!