MySQL 5 - How to select users with their last order number which is calculated on the fly?

Question

I have the data structure as below:

Schema (MySQL v5.7)

CREATE TABLE customers(
  id INT NOT NULL AUTO_INCREMENT,
  name VARCHAR(20),
  PRIMARY KEY (id)
);

INSERT INTO customers (name) VALUES
  ('Wayne Enterprises'),
  ('Star Labs'),
  ('Daily Planet');

CREATE TABLE orders(
  id INT NOT NULL AUTO_INCREMENT,
  customer_id INT,
  order_date DATE,
  order_amount DECIMAL(13,2),
  ship_by VARCHAR(20),
  PRIMARY KEY (id),
  FOREIGN KEY (customer_id) REFERENCES customers(id)
);
 
INSERT INTO orders(customer_id, order_date, order_amount, ship_by) VALUES 
  (1, '2018-11-14', 100.00, "Robin"),
  (2, '2018-11-15', 200.00, "The Flash"),
  (3, '2018-11-15', 150.00, "The Flash"),
  (1, '2018-11-21', 110.00, "The Flash"),
  (2, '2018-11-22', 175.00, "The Flash"),
  (2, '2018-11-22', 175.00, "Cyborg");

---

I use this query to number the order, counted for each customer because the MySQL 5.7 doesn't have some useful functions like RANK, ROW_NUMBER :(

Order numbering

SELECT 
    c.id as cus_id,
    c.name as customer_name,
    o.id as o_id,
    @order_number:=IF(@current_customer = o.customer_id,
        @order_number + 1,
        1) AS order_number,
    o.order_date,
    o.order_amount,
    o.ship_by,
    @current_customer:=o.customer_id AS current_customer
FROM
    orders o LEFT JOIN customers c ON c.id = o.customer_id
    ,(select @current_customer:=null, @order_number:=0) vars
ORDER BY o.customer_id, o.order_date, o.id;

cus_id	customer_name	o_id	order_date	order_amount	ship_by	order_number	current_customer
1	Wayne Enterprises	1	2018-11-14	100.00	Robin	1	1
1	Wayne Enterprises	4	2018-11-21	110.00	The Flash	2	1
2	Star Labs	2	2018-11-15	200.00	The Flash	1	2
2	Star Labs	5	2018-11-22	175.00	The Flash	2	2
2	Star Labs	6	2018-11-22	175.00	Cyborg	3	2
3	Daily Planet	3	2018-11-15	150.00	The Flash	1	3

---

Now I am looking for a way to select all customers with their highest order_number that shipped by "The Flash". The expected query result, which corresponds to the above example data:

cus_id	customer_name	o_id	o_num
1	Wayne Enterprises	4	2
2	Star Labs	5	2
3	Daily Planet	3	1

I tried and ended with sub-query problems which stop me for a couple of days already. Could anyone help?

View on DB Fiddle