WooCommerce: How can I get orders with a custom ID in order meta data object?

You would add the meta_query portion to your wc_get_orders() as the only filter …

function woocommerce_account_orders( $current_page ) {
    $current_page    = empty( $current_page ) ? 1 : absint( $current_page );
    $customer_orders = wc_get_orders( apply_filters( 'woocommerce_my_account_my_orders_query', array(
        'page'     => $current_page,
        'paginate' => true,

        'meta_query' => array(
            array(
                'key' => 'mycustom_id',
                'value' => get_current_user_id(),
                'compare' => '='
            )
        )

    ) ) );

    wc_get_template(
        'myaccount/orders.php',
        array(
            'current_page'    => absint( $current_page ),
            'customer_orders' => $customer_orders,
            'has_orders'      => 0 < $customer_orders->total,
        )
    );
}

This basically says get all the orders where order meta_key = 'mycustom_id' and meta_value = $current_user_id.