Since I didn't want to rip up the trim again if I had to replace a ripped screen (the old screen was stapled underneath the trim work), and with a new dog I figured that would be inevitable, I wanted to devise a way to make replaceable screen panels for each of the sections.
Since I had never made screen panels before, or renovated a screened in porch for that matter, I spent a couple of days staring at the structure trying to figure out my best course of action.
I decided to screw pieces of 1x2, again pressure treated of course, lengthwise on the posts that were flush with the outside edge (before adding the new trim), to serve as stops for the panels I would eventually create. Once the new trim was installed, this would create a nice recess area so the panels would be flush with the outside edge. See the photo above that shows the stops after the new trim was installed.
As the wood was thin - I was using 1x2 after all and screwing it in from out outside edge - I predrilled the holes and used trim head screws so I wouldn't split the wood in two when installing the stops.