Parameters in user-defined aggregate final functions

I am creating a user-defined aggregate function that needs an additional parameter. More precisely it is a cumulative (aka window) minimum that takes as second parameter a time interval defining the window. Since the aggregate function operates on my user-defined data types I have conveyed a dummy example that concatenates the n last values of a text column. I am aware that I can solve this dummy problem in PostgreSQL but the purpose of the example is only to highlight my problem.

CREATE FUNCTION lastNconcat_transfn(state text[], next text, n integer)

    RETURNS text[] AS $$

    BEGIN

        RETURN array_append(state, next);

    END;

    $$ LANGUAGE plpgsql IMMUTABLE STRICT PARALLEL SAFE;

CREATE FUNCTION lastNconcat_combinefn(state1 text[], state2 text[], n integer)

    RETURNS text[] AS $$

    BEGIN

        RETURN array_concat(state1, state2);

    END;

    $$ LANGUAGE plpgsql IMMUTABLE STRICT PARALLEL SAFE;

CREATE FUNCTION lastNconcat_finalfn(state text[], n integer)

    RETURNS text AS $$

    DECLARE

        card integer;

        result text;

    BEGIN

        result := '';

        card := array_length(state, 1);

        FOR i IN greatest(1,card-n+1)..card

        LOOP 

            result := result || state[i];

        END LOOP;

        RETURN result;

    END;

    $$ LANGUAGE plpgsql IMMUTABLE STRICT PARALLEL SAFE;

CREATE AGGREGATE lastNconcat(text, integer) (

    SFUNC = lastNconcat_transfn,

    STYPE = text[],

    INITCOND = '{}',

    COMBINEFUNC = lastNconcat_combinefn,

    FINALFUNC = lastNconcat_finalfn,

    PARALLEL = SAFE

);

I receive the following error

ERROR: function lastnconcat_finalfn(text[]) does not exist

SQL state: 42883

How to tell PostgreSQL that my final function also needs a parameter? I am working on PostgreSQL 10.1. I know that according to the documentation direct parameters are only allowed for ordered-set aggregates, but I would also need a direct parameter for "normal" aggregates.

Notice that the solution proposed here 

is neither ideal nor efficient.

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