Hello,
I have worked on many GIS projects and I have experience with QGIS, PostGIS, various formats (SHP, GeoJSON, KML), libraries (shapely, pyproj, rtree, fiona - all Python) and mapping platforms (Google, Here, OSM).
For this project I would write a Python script that loads the govenrment databases into memory and then goes trough the collected lat/lng matching the closest available data.
Regarding the time I think it will take around 8 hours but I'll have to check all the input data in more detail.
Best wishes,
iticus