I had to make a few more changes to get it to work. On line 53 of ezpages2.php it should say

Code:
  zen_href_link(FILENAME_EZPAGES, 'id='
(without EZPAGES2)

The page_query that decides which EZ Page goes into which box wasn't working, because they both had the same name, so I renamed the second to $page_query2

And I had to add

define('BOX_HEADING_EZPAGES2','Box 2 Heading');

to ez_pages_definitions.php

And now it works a treat!

Would it be worth making it a contrib?