Unless you are working with an exact finished size of the quilt I have to calculate based on the ease of cutting the initial square for the 9 patch. If you work from the other direction then your cut pieces may require weird sizes which I don't want to have to do. So consider this:
If you want a 12" finished block, then the D9P will end up being 11.5" Therefore you loose 1/2" on the finished size when making it D9P.
In your example of wanting a finished 13" finished block (13.5" unfinished)
Each square for the initial 9 patch should be cut 4.83" which is a little over 4 3/4". So the decision when cutting should be to cut the squares at 5" (up a bit) or down to 4.34". So your decision whould be to make the quilt a couple inches larger or smaller than intended.
So my point is to make it easy and make your calculatations based on the regular 9 patch and not what it will be as a D9P. Is it time to take an Excedrian at this point.
I'm wrestling with this right now for a project for a class and trying to decide how many squares to cut and what size.
Regardless of the size you still begin working with a block that is divided by 3.