Thanks for the hint, I was able to find what I needed based on your xml. I was missing this... bjr.NAME becoming the name of the deploy job or batch job if it's set.
left join batch_job_run bjr on bjr.job_run_id = jre.job_run_id
left join job bj on bj.job_id = bjr.batch_job_id and bj.job_version_id = bjr.job_version_id
Deploy jobs are batch jobs. they contain the individual phases as jobs.