Very poor performance with Nested Loop Anti Join

CREATE TABLE onp_crm_person(    id serial PRIMARY KEY,    onp_user_id bigint references onp_user(id) deferrable initially deferred,    is_resource boolean not null default false,    UNIQUE(onp_user_id)
);

CREATE TABLE onp_crm_activity_log(    id bigserial PRIMARY KEY,    relation_id integer REFERENCES onp_crm_relation(entity_id),    logged_for int references onp_crm_person(onp_user_id),    duration bigint
);

CREATE TABLE onp_crm_invoice(    entity_id bigint PRIMARY KEY REFERENCES onp_crm_entity(entity_id),    status_key VARCHAR NOT NULL,    credit_against bigint REFERENCES onp_crm_invoice(entity_id),    sent_date DATE,    UNIQUE(credit_against) deferrable INITIALLY DEFERRED
    -- invoice_print_template_id is added after creation of origo_invoice_print_template
);

CREATE TABLE onp_crm_invoice_line (    id         SERIAL PRIMARY KEY,    invoice_id INTEGER NOT NULL REFERENCES onp_crm_invoice (entity_id)
);

CREATE TABLE onp_crm_calendarentry_invoice_membership(    invoice_line_id INTEGER NOT NULL REFERENCES onp_crm_invoice_line(id) ON DELETE CASCADE,    calendar_entry_id INTEGER NOT NULL REFERENCES onp_crm_activity_log(id),    unique(invoice_line_id, calendar_entry_id) DEFERRABLE INITIALLY DEFERRED
);

explain analyze
SELECT
      log.relation_id as company_id    , sum(log.duration) AS duration
FROM onp_crm_activity_log log
    JOIN onp_crm_person logfor ON logfor.onp_user_id = log.logged_for AND logfor.is_resource = FALSE

WHERE 1 = 1
      -- Filter out already invoiced before 2016-06-27
      AND NOT EXISTS(    SELECT * FROM onp_crm_calendarentry_invoice_membership cem        JOIN onp_crm_invoice_line il ON cem.invoice_line_id = il.id        JOIN onp_crm_invoice inv ON il.invoice_id = inv.entity_id    WHERE cem.calendar_entry_id = log.id          AND inv.status_key = 'INVOICE_STATUS_INVOICED'
          AND inv.sent_date <= '2016-06-27'
          AND NOT EXISTS(        SELECT * FROM onp_crm_invoice creditnote        WHERE il.invoice_id = creditnote.credit_against              AND creditnote.status_key = 'INVOICE_STATUS_INVOICED'
              AND creditnote.sent_date <= '2016-06-27'
    )
)

GROUP BY
    log.relation_id
;