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Do the 30+ people who've viewed this question think it answered itself? I tried to be thorough, but was it too much to read? Or... Is this not a great place to ask such a question?

I've now fixed this issue by refactoring our child theme so the WP queries occur before the header (inserting the content later).

Because we're using a custom homepage template for the front page and a custom "category page" template, I've also had to modify Yoast's "canonical" and "adjacent_rel_links" functions to understand the pagination for those pages (otherwise Yoast simply detects these as "singular" pages and only applies the rel canonical pointing to page 1, regardless of the current page).

I used the following code to allow overriding Yoast in my child-theme's functions.php:

if (defined('WPSEO_VERSION')) {
    function custom_wpseo_override() {

global $wpseo_front;

remove_action('wpseo_head', array($wpseo_front, 'canonical'), 20);
    add_action('wpseo_head', 'custom_wpseo_canonical', 20);
    remove_action('wpseo_head', array($wpseo_front, 'adjacent_rel_links'), 21);
    add_action('wpseo_head', 'custom_wpseo_adjacent_rel_links', 21);
    }
    add_action('init','custom_wpseo_override');
}