Thanks for help. With your hint of a probable misconfiguration somewhere, I discarded the whole environment and recreated it from ansible. It worked immediately. Should have done it before, but I guess I was too dispirited. I worked hard to recreate my 127.0.0.1_only binding problem, to understand what was wrong. And again did not succeed. I suspect something wrong had been changed/added in one of the jvm* files.
So it confirms your view that cassandra-env.sh does the configuration through LOCAL_JMX, and nothing else is necessary.
Thanks for help. All the best. Alain