"after the 12th there will be a line break inserted and the 13th item will be forced into the next row. I can't figure out where the break is being inserted in the code, but it should be possible to manually remove it."
The output goes through /includes/templates/your_template/common/tpl_columnar_display.php, where this is inserted at the end of every row's output (near the bottom of the file):
<br class="clearBoth" />
You would need to selectively remove that when the new products centerbox is being processed and not otherwise.
An easier alternative would be to add to your stylesheet
Code:
#whatsNew br.clearBoth {display: none;}