evening Jamie;
inline script with "nonce" or "post_id" in it gets automatically excluded from optimization, to avoid the "random" strings in them to break the autoptimize's cache. in your case I indeed see;
"update_shipping_method_nonce":"534f904eea"(and there's a nonce in the other inline JS block as well) Not excluding that from optimization would result in AO having to re-aggregate & -minify the JS for the cart-page every time the nonce changes, slowing things down & leading to a huge amount of cached JS.
there are four approaches you can take to fix the page;
1. force JS into head
2. exclude jquery.js from optimization
3. use the API to disable AO on /cart/ (see example code in autoptimize_helper.php_example)
4. make a small change to your footer template, adding a "js insert marker" and using the API to tell AO to insert JS at that marker instead of before the closing body tag (again see example code in autoptimize_helper.php_example)
hope this helps,
frank