The optimization process and recommendations:

1. Avoid Subqueries (query line: 27): We advise against using subqueries as they are not optimized well by the optimizer. Therefore, it's recommended to join a newly created temporary table that holds the data, which also includes the relevant search index.
2. Explicitly ORDER BY After GROUP BY (modified query below): By default, the database sorts all 'GROUP BY col1, col2, ...' queries as if you specified 'ORDER BY col1, col2, ...' in the query as well. If a query includes a GROUP BY clause but you want to avoid the overhead of sorting the result, you can suppress sorting by specifying 'ORDER BY NULL'.

The optimized query:

WITH t1 AS (SELECT
        a.id,
        AVG(standard_qty) std_avg,
        AVG(poster_qty) pos_avg,
        AVG(glossy_qty) gloss_avg 
    FROM
        accounts a 
    JOIN
        orders o 
            ON a.id = o.account_id 
    GROUP BY
        1 
    ORDER BY
        NULL), t2 AS (SELECT
        MAX(t1.std_avg) max_std_avg,
        MAX(t1.pos_avg) max_pos_avg,
        MAX(t1.gloss_avg) max_gloss_avg 
    FROM
        t1) SELECT
        std_id,
        t2.max_std_avg,
        pos_id,
        t2.max_pos_avg,
        glos_id,
        t2.max_gloss_avg 
    FROM
        (SELECT
            (SELECT
                t1.id std_id 
            FROM
                t1,
                t2 
            WHERE
                t1.std_avg = t2.max_std_avg),
            (SELECT
                t1.id pos_id 
            FROM
                t1,
                t2 
            WHERE
                t1.pos_avg = t2.max_pos_avg),
            (SELECT
                t1.id glos_id 
            FROM
                t1,
                t2 
            WHERE
                t1.gloss_avg = t2.max_gloss_avg)) foo,
            t1,
            t2