You'll want to use the "%JOBUSER%" token. That should get the information for you. We're setting it in a registry file and then importing that Imaging stamp into the registry and collecting the information with a custom inventory.
You'll want to watch for a couple of gotchas on that.
1. Security has to be enabled
2. If you have a job or task that schedules a 2nd job then the %JOBUSER% token won't work inside the 2nd job.