Move Billing Inputs to Shipping Field

Is there a way to move, for example, billing email into the shipping field without upsetting the meta saving?

For one, this is not an issue about priority. That only works in the same field.

Some people have suggested, assigning one field to another, such as:

$fields['shipping']['billing_email'] = $fields['billing']['billing_email'];
unset($fields['billing']['billing_email']);

But this does not work.

I tried, then, doing above and saving the post meta using hook ‘woocommerce_checkout_update_order_meta’, but this must have changed:

//Billing email
$billing_email = $_POST['billing_email'];
if ( ! empty( $billing_email ) ) {
   update_post_meta( $order_id, 'billing_email', sanitize_text_field( $billing_email ) );

If anyone has any advice how to do this, that’d be great. I’d rather not create a facsimile of the field (i.e., ‘billing_email_copy’) just in case our plugins or third-party shipping applications don’t like that.
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