Hi Hunter,
I see that you are using the 7.10 modeler. Have you tried retrieving the headers from the http response object?
Here is the system domain model
In your rest service, set your response to "store in http response"
and then retrieve the headers via retrieve by association
If you have to use the import mapping. Create a string variable and set the value to
$HttpResponse/Content
and then call the import mapping activity
Hope this helps!