Hello Thomas,
Unfortunately in order to do this it would require custom coding to achieve. There is nothing in the template that gives the ability to do this out of the box. To point you in the right direction you could add the following php and wrap it around the CSS you want to show online on the homepage. This would be placed in the index.php file:
<?php if($s5_pos_custom_1 == "published") { ?>
your homepage only CSS code here
<?php } ?>