Wow that is complicated! Thanks for sharing, it's good to know how time consuming this could be if I take it further.
It sounds like Overpass is the way to get the data I need - once I figure out how to reference it in Overpass (network/relation details).
My current solution is based on OpenMapTiles and uses their stack for creating, and subsequently rendering, vector tiles. First, I obtain an extract of OSM data via the Overpass API. Then I convert it from XML to protobuf, as it's a much more efficient format. Afterwards I import it into a PostGIS database using imposm3 and define some SQL functions that transform that data. Then I generate some vector tile definition from the OMT format into tm2source format. After that I finally generate the vector tiles in mbtiles format using tilelive, server them as GeoJSON using tileserver-gl and style them using maputnik and mapbox-gl styles.
There seems to be some bug with imposm3 and relations, because I can't get them to import. Or I'm just not doing it right.