I'm sure someone will correct me if I'm wrong, but isn't it simpler to manage this sort of functionality by putting a counter in a table and using a CTE to increment it along with the insert? Something like

  with u as (
    update organizations
    set last_external_id = last_external_id + 1
    where id = 123
    returning last_external_id
  )
  insert into incidents (organization_id, external_id, title)
  select 123, last_external_id, 'Blah blah blah'
  from u;

The risk here of course is running into lock contention around the organization table there's a high volume of incident creation for the same organization, but considering the context (incident management) that seems pretty low risk.