I got re-auto-calculation to work on state change by just duplicating some lines in the module, renaming country to zone.

Original:
// click button when country is changed
var selected_country = $("#edit-panes-delivery-delivery-country");
selected_country.change(function(){
shipping_button.click();
});

Copied and changed to:
// click button when state is changed
var selected_state = $("#edit-panes-delivery-delivery-zone");
selected_state.change(function(){
shipping_button.click();
});