Translate sql with nested queries into query builder methods [duplicate]

Question

I have written a SQL query which works fine and output provides all the data that I need:

Please see this screenshot:

This is the SQL code:

SELECT 
    P.name, C.project_id, C.choice_id, C.time_stamp, P.id, 
    P.description, T.type, P.activated
FROM
    (SELECT P.*
     FROM aqoru_pt_project P
     JOIN
         (SELECT id, MAX(creation_date) AS latestUpdate
          FROM aqoru_pt_project
          GROUP BY id) t ON t.id = P.id AND t.latestUpdate = P.creation_date) P
JOIN
    (SELECT C.*
     FROM aqoru_pt_project_choice C
     JOIN
         (SELECT project_id, MAX(time_stamp) AS latestDate
          FROM aqoru_pt_project_choice
          GROUP BY project_id) t ON t.project_id = C.project_id AND t.latestDate = C.time_stamp) C ON P.id = C.project_id
LEFT JOIN 
    aqoru_community_groups_members CGM ON P.group_id = CGM.groupid
INNER JOIN
    aqoru_pt_project_type T ON P.type_id = T.id
WHERE
    P.user_id = 569 OR CGM.memberid = 569
    AND CGM.permissions = 1
    AND P.deactivated != 1
GROUP BY 
    P.id
ORDER BY 
    P.id;

Now I need to push it into php format I was trying without great success as I am struggling mainly with the part where I try to put JOIN in SELECT on the very beginning of the code.

Definitely the part after ON P.id = C.project_id works fine. The problem occurs when I try to add max value from other table.

This is the code I wrote, but it does not work:

public function getProjects($userID)
    {
        $db = JFactory::getDbo();
        $query = $db->getQuery(true);

        $columns = array('P.id', 'P.name', 'P.description', 'T.type', 'P.activated');
        $query
            ->select(array('P.id', 'P.name', 'P.description', 'T.type', 'P.activated', 'max(C.time_stamp) as max'))
            ->from($db->quoteName(
                ->SELECT ('P.*')
                ->FROM ($db->quoteName('aqoru_pt_project', 'P')
                ->JOIN($db->quoteName(
                    ->SELECT ('id', 'MAX(creation_date) AS latestUpdate')
                    ->FROM ($db->quoteName('aqoru_pt_project')
                    ->group($db->quoteName('id')) 't' .  ' ON t.id = P.id AND t.latestUpdate = P.creation_date') P
                ->JOIN(
                  ->SELECT ('C.*')
                  ->FROM ($db->quoteName('aqoru_pt_project_choice', 'C')
                    ->JOIN($db->quoteName(
                    ->SELECT ('project_id', 'MAX(time_stamp) AS latestDate')
                    ->FROM ($db->quoteName('aqoru_pt_project_choice'))
                    ->group($db->quoteName('id')) 't' .  ' ON t.project_id = P.project_id AND t.latestUpdate = P.time_stamp') 'C' . 'ON P.id = C.project_id'

            ))
            ->leftjoin($db->quoteName('#__community_groups_members', 'CGM') . ' ON P.group_id = CGM.groupid')
            ->innerjoin($db->quoteName('#__pt_project_type', 'T') . ' ON P.type_id = T.id')
            ->where(
                $db->quoteName('P.user_id') . ' = ' . $db->quote($userID),
            )
            ->orwhere(array(
                $db->quoteName('CGM.memberid') . ' = ' . $db->quote($userID),
                $db->quoteName('CGM.permissions') . ' = 1'
            ))
            ->andwhere($db->quoteName('P.deactivated') . ' != 1')
            ->group($db->quoteName('P.id'))
            ->order('P.id DESC');
        /*
         * Note: for some reason the queries return duplicates on the production site not on my local site
         * So we must group by projectID to avoid duplicates. I am not aware what is causing this duplication
         */

        return $db->setQuery($query)->loadObjectList();
    }

Problem is definitely when trying to push join to get my MAX in the very beginning of the query, but I have no idea how to proceed with it.