Huw,
Let me start by saying that what I'm about to recommend is something we never recommend or suggest.. making a modification to something that's part of Joomla core. However, in this case, for now (and for a quicker answer), we must.
Basically, what's happening is the the mod_articles_news is calling the content plugins before the articles are rendered. There's actually a mechanism built into the content plugins that let our plugin 'know' where it's being called from (an article view, a module, etc). However, the mod_articles_news module is actually lying, in a way, by saying it's actually the article component. To fix this, our best answer is to simply comment out the line this is occuring on, so it doesn't call the content plugins at all.
If this makes no sense, no worries. I just need to explain the background. To fix, please edit the following file:
/modules/mod_articles_news/helper.php
At line 92, you'll see the below line:
$results = $app->triggerEvent('onContentBeforeDisplay', array('com_content.article', &$item, &$params, 1));
Please comment this line out by putting a hash '#' sign at the beginning of it.
That should fix you right up, but it will prevent the content plugins from being called in that module, which may cause other issues. Please let us know if it does, and good luck!
Alex