Why doesn't Per Product shipping make my order total go up?

That's how Per Product mode works. Wcart treats each product's Shipping cost as part of its selling price. At checkout it shows that amount as a separate shipping line and lowers the subtotal by the same amount, so the grand total stays the same.

So with Per Product, set your product price to include shipping.

If you want shipping added on top of the price instead, go to Settings → Store Settings → Shipping Setup, set Shipping Type to Overall Product, enter a Shipping Cost and click Save Changes. That flat amount is added once per order.