Let me know if I am missing somethingIf your requirement is that the user may edit one of the Sub Payroll records related to a Job from the Jobs form, the solution can be quite easy.
A way that you could do this is by adding a Report Link field in the Jobs table where Jobs: Related Sub Payroll matches the value in the field Sub Payroll: Record ID#.
You could then add this report link to the form, choose the Display the related records directly on the form radio button, and check the Editable checkbox.
Make sure that the report that the display is based upon has the Completed By field selected as one of the columns.
The end result should be an embedded report of all related Jobs where you can select the Completed By drop down on any of those records. This solution is not perfect and there is a risk of the end user dealing with some strange errors, but this could work.
If that is not the case and you need to edit the drop down from the Production Task form or a Report within the Job or Production Task table, the complexity of the problem expands a bit and you'll need a much more creative solution.