Shipping class costs not working

I am working with a client that is using WooCommerce and I have set two methods and one shipping class. Here is the end goal:

Offer/Set Flat Rate $5 on all orders
Offer/Set Free Shipping on all carts over $50
Set Free Shipping on the two stickers they have in stock

Everything works except the Ship[ping class I assigned to the two sticker products they have.
I even set two shipping classes:
free-sticker-shipping
All-other-items

I set the free class to the two stickers and the All-other-items to everything else they have but it still calculates the $5 for only having stickers in the cart.

The page I need help with: [log in to see the link]