"I need to Create a CUSTOMER as the PARENT Customer, "Shiloh National Parks" "

Yes. Open the Customer Center, make sure you are viewing that in Hierarchical View, and Add that customer name.

"then move the existing customer to a JOB"

Yes; pause the cursor on the little handle to the left of the Name, to see your mouse become a Four-Headed arrow. Click and drag it Under, then to the Right = Indent, under the new Customer Name. This = Demoted to be Job.

"How do I do This, seeing that there is no drop down list on the upper right hand side for edit customer job screen?"

That only shows up with Edit Job.