I managed to solve this issue, so if anyone is interested, I’ll show what I did below.
I placed the aforementioned DIV in the WooCommerce plugin’s wocommerce-template.php file, in the first function on line 29 (woocommerce_content). I placed it on line 46, so that it was in the ‘else’ part of the if statement that checks whether or not the page is a single product.
This means that it will only show up on main pages, not single product pages.
I hope this helps someone.