Postgresql – How to parallelise remote queries in Postgres

I am querying N tables remotely using dblink.
This queries represent a sort of "sharding" of the data.
Each remote query takes roughly the same time (~ 0.5 sec).

However when I gather all the data in one query for a simple count(*) using either join, union all or CTE/with the total amount of time became "linear" which means 0.5*N.

That of course kills a lot of the purpose for the "sharding" process.

Is there any way to force Postgres (11) to gather the data in parallel instead of sequentialising it?

UPDATE

The remote query I am running on the single "shard" is based on a function that wraps a single spatial query along with an aggregation and it uses indexes and partitions (spatial query along with an aggregation):

CREATE OR REPLACE FUNCTION my_func(pt character(1), bd smallint, polyg geometry, tf date, tt date) RETURNS
TABLE(import_date date, bedrooms smallint, property_type character(1),
      .....,r_rent_paid float[]) AS $$
BEGIN
    RETURN query
    select
          coalesce(s.import_date, r.import_date) as import_date,
          coalesce(s.bedrooms, r.bedrooms) as bedrooms,
          coalesce(s.property_type, r.property_type) as property_type,
          s.s_size,
          .....,
          r.rent_paid
    from
    (
        select

           sc.import_date,
           sc.bedrooms,
           sc.property_type,

           ......multiple percentile_cont......,

           percentile_cont(array[0.25,0.5,0.75,0.9]) within group (order by sc.discount) filter(where sc.discount > 0) as discount

           from node.sales sc
           where sc.property_type = pt and  sc.bedrooms = bd and st_Intersects(polyg,sc.geom)
           and sc.import_date between tf and tt
           group by sc.import_date, sc.bedrooms, sc.property_type
    ) s
    full join
    (
        select
           rc.import_date,
           rc.bedrooms,
           rc.property_type,

           ......multiple percentile_cont......,


           percentile_cont(array[0.25,0.5,0.75,0.9]) within group (order by rc.asking_rent_sqft) filter(where rc.asking_rent_sqft > 0) as rent_paid_sqft

           from node.rents rc
           where rc.property_type = pt and  rc.bedrooms = bd and st_Intersects(polyg,rc.geom)
           and rc.import_date between tf and tt
           group by rc.import_date, rc.bedrooms, rc.property_type
    ) r
    on r.import_date = s.import_date and r.bedrooms = s.bedrooms and r.property_type = s.property_type;
END $$ language plpgsql;

I have tried to run this functions using postgres_fdw creating this function only on the "master" and running it like this:

select import_date, bedrooms, property_type, count(*)
from (
SELECT * FROM my_func(…point import foreign schema shard-1…)
union all
SELECT * FROM my_func(…point import foreign schema shard-2…)
union all
…. 6 more
) K
GROUP BY import_date, bedrooms, property_type;

However the call is blocking for each select so it kills the process.

As alternative so far I tried using dblink as it create no blocking queries (async):

SELECT dblink_connect('dtest1', 'host=xxxx ....');
SELECT dblink_connect('dtest2', 'host=xxxx ....');
.....
SELECT dblink_connect('dtest8', 'host=xxxx ....');

SELECT dblink_send_query('dtest1', 'select * from my_func(...)');
SELECT dblink_send_query('dtest2', 'select * from my_func(...)');
.....
SELECT dblink_send_query('dtest8', 'select * from my_func(...)');

and finally:

select import_date, bedrooms, property_type, count(*)
from (
    SELECT * FROM dblink_get_result('dtest1') AS t1(....)
    union all
    SELECT * FROM dblink_get_result('dtest2') AS t2(....)
    union all
    .....
    union all
    SELECT * FROM dblink_get_result('dtest8') AS t8(....)
) K
GROUP BY import_date, bedrooms, property_type;

which is still going "linear" and if I run the query soon after the first run it may no return results (unless I wait a few seconds from the previous).

UPDATE 2

What is look a working solution so far is what @Richard Huxton suggested, about using PL/Proxy which allows to run remote functions (in parallel when you use Cluster/RUN ALL). I have also tried CITUS but I could not get the "parallel/run" (percentile_cont is not supported and also won't change the concept of having a single machine with a table partitioned for that specific case as you have to pass through the query planner.