I am trying to add Job Head fields to the Issue Material screen so we can make a note about the date/time the material was pulled from the freezers. I used FKV to get access to the fields but they are all set to read only. Is there a way to change these?
No, it is a view only.
If you want to update these fields, you will need to do it with custom code.
I knew it was seeming too easy 
Any ideas on how to capture the data on the entry screen? Should I use the CallContextBPMData fields and then use a BPM to assign those to the JobHead fields I need.
You could go the CallContextBPMData route. You could also just take the reference and datestamp fields from Issue Material and directly push that in a post-proc BPM.
Personally, I only use the CallContext fields when I’m navigating the user between screens in a single process. Like, user does X, which triggers a call to LaunchForm, and I pass any arguments that don’t fit in that method to CallContext, which then prepopulates fields in the next screen.
If I’m just updating data in the background, I tend to use the fields directly.