I received a response from tech support. This fixed my issue:
1. Please make sure you have checked shipping for all the products
2. Set the weight of all products to 0
3. Select the container as small box (or anything else, but it should
be same for all the products in your case)
4. Set the container capacity to 10000 or something high
5. In Admin > Shipping Settings, set the weight of small box to 1 and price to 0
6. Enter domestic price per ounce to 5 and international to 30