I have set up zones and shipping by quantity.
When you first go to the checkout screen, you are presented with a list of shipping options (but no prices), until you select "Calculate Shipping".
However, if you do not click "Calculate shipping", and instead just select a shipping method (without a price), you get free shipping. Not cool.
Additionally, if you do those same steps, then go BACK to the cart, the shipping method is not the same as you initially chose.