FWIW, if you fight through the "undocumented features," Jenkins actually ends up being one of the best tools out there to manage via Ansible or whatnot. The Groovy/Java API for Jenkins is incredibly powerful, and by adding Groovy scripts to the /var/lib/jenkins/init.groovy.d/ directory, you can configure just about anything.

Maybe this will be helpful? Here's the Ansible config I've built for a Jenkins deployment I manage: https://github.com/HHSIDEAlab/hhsdevcloud-ansible/tree/maste.... Most of the "meat" is in the Groovy scripts in the templates/ directory there.