Changing the tax class on checkout page via dropdown in WooCommerce

Question

Have been trying to solve this for a couple days and decided to just break down and ask for some insight. I'm basing what I have off of these two solutions:

Change items tax rate in WooCommerce checkout based on radio buttons

Add a dynamic fee based on a select field in WooCommerce Checkout

I'm trying to use a drop down/select to change the tax class on the checkout page of WooCommerce.

I've left a lot alone from the two above examples but am still not getting the results expected. I also need to store & place the delivery location in the admin area & emails but need to get this tax class change issue sorted first.

Below is what I have right now. It seems like it should be working but alas, no joy.

// Add a custom select fields for packing option fee
add_action( 'woocommerce_after_order_notes', 'checkout_shipping_form_packing_addition', 20 );
function checkout_shipping_form_packing_addition( ) {
    $domain = 'woocommerce';

    echo '<tr class="packing-select"><th>' . __('Pickup Location', $domain) . '</th><td>';

    $chosen   = WC()->session->get('chosen_packing');

    // Add a custom checkbox field
    woocommerce_form_field( 'chosen_packing', array(
        'type'      => 'select',
        'class'     => array( 'form-row-wide packing' ),
        'options'   => array(
            ''    => __("Please select a location...", $domain),
            'BELGIUM - LOC' => sprintf( __("BELGIUM - LOC", $domain) ),
            'BROOTEN - LOC' => sprintf( __("BROOTEN - LOC", $domain) ),
            'OWATONNA - LOC' => sprintf( __("OWATONNA - LOC", $domain) ),
        ),
        'required'  => true,
    ), $chosen );

    echo '</td></tr>';
}

// jQuery - Ajax script
add_action( 'wp_footer', 'checkout_shipping_packing_script' );
function checkout_shipping_packing_script() {
    // Only checkout page
    if ( is_checkout() && ! is_wc_endpoint_url() ) :

    WC()->session->__unset('chosen_packing');
    ?>
    <script type="text/javascript">
    jQuery( function($){
        $('form.checkout').on('change', 'select#chosen_packing', function(){
            var p = $(this).val();
            console.log(p);
            $.ajax({
                type: 'POST',
                url: wc_checkout_params.ajax_url,
                data: {
                    'action': 'woo_get_ajax_data',
                    'packing': p,
                },
                success: function (result) {
                    $('body').trigger('update_checkout');
                    console.log('response: '+result); // just for testing | TO BE REMOVED
                },
                error: function(error){
                    console.log(error); // just for testing | TO BE REMOVED
                }
            });
        });
    });
    </script>
    <?php
    endif;
}

// Php Ajax (Receiving request and saving to WC session)
add_action( 'wp_ajax_woo_get_ajax_data', 'woo_get_ajax_data' );
add_action( 'wp_ajax_nopriv_woo_get_ajax_data', 'woo_get_ajax_data' );
function woo_get_ajax_data() {
    if ( isset($_POST['packing']) ){
        $packing = sanitize_key( $_POST['packing'] );
        WC()->session->set('chosen_packing', $packing );
        echo json_encode( $packing );
    }
    die(); // Alway at the end (to avoid server error 500)
}

// Add a custom dynamic packaging fee
add_action( 'woocommerce_before_calculate_totals', 'change_tax_class_conditionally', 1000 );
function change_tax_class_conditionally( $cart ) {
    if ( is_admin() && ! defined( 'DOING_AJAX' ) )
        return;
    
    if ( did_action( 'woocommerce_before_calculate_totals' ) >= 2 )
        return;

    $domain      = "woocommerce";
    $packing_fee = WC()->session->get( 'chosen_packing' ); // Dynamic packing fee

    if ( $packing_fee === 'BELGIUM - LOC' ) {
        //$label = __("Bag packing fee", $domain);
        $tax_class  = '5 Percent';
    }
    if ( $packing_fee === 'BROOTEN - LOC' ) {
        //$label = __("Bag packing fee", $domain);
        $tax_class = '0 Percent';
    } 
    if ( $packing_fee === 'CHER-MAKE - LOC' ) {
        //$label = __("Bag packing fee", $domain);
        $tax_class  = 'Reduced Rates';
    } 

    // Loop through cart items
    foreach( $cart->get_cart() as $cart_item ){
        if( $choice === $field_value ) {
            $cart_item['data']->set_tax_class($tax_class);
        }
    }
}

// Field validation, as this packing field is required
add_action('woocommerce_checkout_process', 'packing_field_checkout_process');
function packing_field_checkout_process() {
    // Check if set, if its not set add an error.
    if ( isset($_POST['chosen_packing']) && empty($_POST['chosen_packing']) )
        wc_add_notice( __( "Please choose a packing option...", "woocommerce" ), 'error' );
}