@Milo’s answer worked perfectly (see comment above).
if (in_array($post->ID, $do_not_duplicate)) continue; meant that duplicate posts were still being counted in the loop, though not being displayed.
To fix, remove this line, and exclude duplicate posts from the query with this argument:
'post__not_in' => $do_not_duplicate.
Thank you @Milo for your swift and succinct response.
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