> * one COPY per bulk (20 000 rows) copy does not fit so well, as it is not only initial populating.
Why do you say COPY doesn't fit? It seems to me that COPY fits perfectly for your case, and would certainly make the load faster.
I suspect (not sure though) that the degradation is most because you are inserting one row at a time, and, it needs to verify FSM (Free Space Map) for each tuple inserted, when the table start to get more populated, this verification starts to become slower. If that is really the case, COPY would certainly improve that, or even INSERT with many rows at once.