Update Option Stored in Multi-Dimensional Array

I have data in the wp_options table currently stored as a multi-dimensional array (profile_element_order):

a:12:{s:17:"img_base64_enable";s:1:"1";s:25:"moulding_combination_page";s:0:"";s:24:"moulding_collection_page";s:0:"";s:25:"idea_gallery_thumb_height";s:3:"200";s:24:"idea_gallery_thumb_width";s:3:"200";s:23:"collection_thumb_height";s:3:"200";s:22:"collection_thumb_width";s:3:"200";s:20:"profile_item_columns";s:1:"4";s:17:"idea_item_columns";s:1:"2";s:24:"collections_item_columns";s:1:"2";s:25:"combinations_item_columns";s:1:"4";s:21:"profile_element_order";a:5:{i:0;s:8:"Option 1";i:1;s:8:"Option 2";i:2;s:8:"Option 3";i:3;s:8:"Option 4";i:4;s:8:"Option 5";}}

What I’m trying to accomplish is update the profile_element_order option (within those options). Here’s how everything looks so far:

function psort_save_order() {

    global $mouldings_options;

    $list = $mouldings_options['profile_element_order'];
    $new_order = $_POST['list_items'];
    $new_list = array();

    // update order
    foreach($new_order as $v) {
        if(isset($list[$v])) {
            $new_list[$v] = $list[$v];
        }
    }

    // save the new order
    update_option('profile_element_order', $new_list);

    die();
}
add_action('wp_ajax_psort_update_order', 'psort_save_order');

The data is correctly posting to the DB table (as I can see some of my failed attempts as new option entries, like mouldings_settings->profile_element_order) — I’m just having a hard time figuring out the update_option() syntax for just that specific option. I’ve tried things like (bearing in mind `mouldings_settings is the actual option name):

mouldings_settings['profile_element_order']
$mouldings_options['profile_element_order']
profile_element_order

but no dice at the moment. Any pointers would be greatly appreciated! Thanks!

Update
This is what I have now — ajax action saves fine, but when I save the plugin options, it duplicates the options in the database and throws up the same error as before:

a:17:{s:17:"img_base64_enable";s:1:"1";s:25:"moulding_combination_page";s:0:"";s:24:"moulding_collection_page";s:0:"";s:25:"idea_gallery_thumb_height";s:3:"200";s:24:"idea_gallery_thumb_width";s:3:"200";s:23:"collection_thumb_height";s:3:"200";s:22:"collection_thumb_width";s:3:"200";s:20:"profile_item_columns";s:1:"4";s:17:"idea_item_columns";s:1:"2";s:24:"collections_item_columns";s:1:"2";s:25:"combinations_item_columns";s:1:"4";s:21:"profile_element_order";a:5:{i:4;s:8:"Option 5";i:0;s:8:"Option 1";i:1;s:8:"Option 2";i:3;s:8:"Option 4";i:2;s:8:"Option 3";}i:0;s:8:"Option 5";i:1;s:8:"Option 1";i:2;s:8:"Option 2";i:3;s:8:"Option 4";i:4;s:8:"Option 3";}

Function:

function psort_save_order() {

    global $mouldings_options;

    $list = $mouldings_options['profile_element_order'];
    $new_order = $_POST['list_items'];
    $new_list = array();

    // update order
    foreach($new_order as $v) {
        if(isset($list[$v])) {
            $new_list[$v] = $list[$v];
        }
    }

    $mouldings_options['profile_element_order'] = $new_list;
    $mouldings_options = array_merge($mouldings_options,$mouldings_options['profile_element_order']);

    // save the new order
    update_option('mouldings_settings', $mouldings_options);

    die();
}
add_action('wp_ajax_psort_update_order', 'psort_save_order');