We needed to disable all of Drupal’s CSS files from our theme. Here’s how we did it:

function THEMENAME_preprocess(&$variables) {

  // Get rid of all of Drupal's CSS files
  $css = drupal_add_css();
  foreach ($css['all']['module'] as $file => $status) {
    if (!strstr($file, 'modules/MYMODULE')) {
      unset($css['all']['module'][$file]);
    }
  }
  $variables['styles'] = drupal_get_css($css);

We also wanted (no *real* need) to use screen.css rather than style.css, so we edited THEMENAME.info to have this:

stylesheets[all][] = reset.css
stylesheets[all][] = screen.css

… and we removed the line for style.css from it.

Finally, as the superuser we went to /admin/build/modules (or /themes, can’t remember now) to refresh the theme cache. We also had to tick to enable the theme at /admin/build/themes as although we’d been using the theme for ages quite fine, it wasn’t actually ticked before.

And hey presto, it worked. Should probably add that it took waaaay too long to do though, so though we’d add this snipped for others to read.