This would make pre-generating the data a lot easier, as a simple file can be built by CI and then fetched by the server with no Postgres DB required. Tegola supports serving data from GeoPackages.
There are some wrinkles here - the one I spotted is that GPKG/SQLite doesn't support array types, which are output by GDAL now for DXF extended attributes.
Perhaps the best approach is to load the DXF data into memory in python using the GDAL python bindings, perform the processing there, and then write out a nice clean table into the GeoPackage without any of the DXF mess.