The query burns down to just:

SELECT *
FROM  ( 
   SELECT DISTINCT ON (initial_record_id)
   FROM   marketplace_messages
   ORDER  BY initial_record_id, id DESC
   ) sub
ORDER  BY id DESC;

The tricky bit is that leading ORDER BY expressions must cover DISTINCT ON expressions. So sort a second time in the outer query.

See:

• PostgreSQL DISTINCT ON with different ORDER BY
• Select first row in each GROUP BY group?