Nominatim already yields two identifiers for a location called place_id and osm_id. If you won’t find them back in the PostgreSQL database already, we might want to add them. Please let us know.
We might think about investigating the issue in order to aim at fixing it within Luftdatenpumpe. The problems you are observing will probably also hit others and in that manner, we can do better for the whole community out there.
In order to get the ball rolling, we created a topic to discuss the situation and a corresponding issue on GitHub. Feel free to comment on both of them as you like.