I was able to temporarily fix the issue on the UPS plugin by finding where the calculate_shipping function was declared and updating the function signature to match the documentation [0]: public function calculate_shipping( $package = array() ). For the UPS plugin it was located at [1] on line 879.
[0] https://docs.woothemes.com/wc-apidocs/source-class-WC_Shipping_Method.html#138-141
[1] plugins/woocommerce-shipping-ups/includes/class-wc-shipping-ups.php
