oops. Then of course there’s this here, which answers my question and makes the initial idea possible:
http://codex.ww.wp.xz.cn/Giving_WordPress_Its_Own_Directory
Let me answer that myself.
It was a bad idea to remove the .php page from the wordpress directory. I’ve moved it into there and now the 2nd/3rd and so on pages work. (All the static html pages are still in the root dir, which is fine)
Also, the bit at the top needs to say:
<?php
// Include WordPress
define('WP_USE_THEMES', false);
require('wp-blog-header.php');
?>
