Tommy,
WELCOME TO THE AWS WELDING FORUM!!
Now, I hate to try and add anything to Al's comments. He is far more experienced and knowledgable in these things than I.
But, let me see if I understand the question...
You are wondering if you can take a procedure that is 'Pre-qualified' in D1.3 or Qualified to the simple tests OF D1.3 and then call them 'Pre-qualified per D1.1???
If you are wondering about the overlapping of materials dimensions between the max size in D1.3 and the min size in D1.1, that does not allow one to take a procedure from one code and apply it to another code. Each must be used and is applicable only within it's own scope and application.
As Al points out...D1.1 to D1.1 & D1.3 to D1.3. You can't try to work them together to get a Pre-qualified WPS when you actually need the PQR and testing requirements of Clause 4 in D1.1.
I hope I made sense.
Have a Great Day, Brent