Thank you Dmitry!
This did the trick, however: the styling looks like crap. What's the best approach to edit this styling? (and possibly a little bit of the attributes html)
Because of multiple reasons we had to roll back to 1.9, and it seems a lot harder to move the attributes next to the product.
Could you please help? I'll be forever thankful. Spent the enter morning looking for a solution but couldn't find a descent one yet.
Last thing I tried was manually adding
<?php echo $this->getChildHtml('additional') ; ?>
But that's just messy and it also displays the "Additional Information" title.