I wrote the original kmb32123/youtube-dl-server. I just added an environment variable, YDL_UPDATE_TIME, that you can set to 'False' to disable using the server modified date. Something like these:
docker run -d -e YDL_UPDATE_TIME=False kmb32123/youtube-dl-server
YDL_UPDATE_TIME=False python3 -u ./youtube-dl-server.py