To close this question, what seemed to have worked is indeed running
docker-compose stop
docker-compose rm -f
docker-compose -f docker-compose.yml up -d
I.e. remove the containers before running up again.
What one needs to keep in mind when doing it like this is that data volume containers are removed as well if you just run rm -f. In order to prevent that I specify explicitly each container to remove:
docker-compose rm -f application nginx php
As I said in my question, I don't know if this is the correct process. But this seems to work for our use case, so until we find a better solution we'll roll with this one.