if people are uploading, does that mean there's a database table storing information?
if so, and you have access to the database (mine is a MySQL db, accessed via phpMyAdmin), then you can run a mysql query, put in in some php code and drop it into the ezblock...
in the query, set it to 'Order by rand()' (leave out the ticks)
i do this already on our site, and am now upgrading it to run everything through smf - inc our admin pages. i have tested dropping in full page php/mysql/html coded pages into ezblocks, and they work fine... do remember to leave out the initial <?php and the final ?> in the ezblock