having trouble with shipping classes

On my site, I have 2 kinds of products, small parts and large parts. For small parts, I want to offer USPS First Class and USPS Priority. But if an order contains a large part, I only want to offer USPS Priority.

I’ve set it up so that if I have just a small part in the cart, it shows the two options.

If I have just a large part in the cart, it shows just USPS Priority.

But if I have both a small part and a large part in the cart, it shows both options. This allows users to order a large part with USPS First Class shipping for the price of the small part shipping.

I can’t have that.

I’ve tried a variety of ways to set up the zones but I can’t figure this one out.