Plugin “WP Attachments” outputs after the_content, how can I best change the location?

Without looking into the plugin, it looks like you could first remove the default placement using:

remove_filter('the_content', 'wpatt_content_filter');

and then call the list function somewhere in your template like this:

echo wpatt_content_filter('');

(the remove_filter would be in functions.php or somewhere near the top of your template, ie before the_content() is called.)