Well you already own the thermatru door and sidelights and want to install a storm door over the 36" door. First, the storm door handle could be mounted to the storm door either higher or lower so as not to interfer with the entrance door knob. ,.You can purchase a storm door without the 3 holes for lock assy., make them yourself where they'll work.

Although I'm suprised that the clearnace in your jamb is not enough to install a storm door with hardware, you can do it just like you said. And it won't look hookey.

Extend the casings (rails) as you need to so the S/D can be installed and operate properly. I've had to do it here and there through the years. But you can do it.

A last thought, you can also build out all the casings around the door and the sidelights as it would camouflage the door part.

The Porch Guy

Here is a link that might be useful: My Album

Heres the direction I am heading:
The opening is actually 35", so I am going to buy 36" vinyl screen door (low maintenance is desired) that is 1" thick. On the latch side of the door, I will route a 1/4" inch overlay lip. This will cover the door/rail seam and act as the door stop preventing the screen door from swinging into the front door. I might put a 1/4 round detail on it. I will buy face mounting "self close" screen door hinges, make 1/4" pads to mount under them on the rail side, then screw them to the rails and the door. The door will extend 1/4 inch beyond the door rails and only take up 3/4" of the 1 1/2" space between the rail fronts and the front door. I hope this will not interfere with the existing door hardware. If it does, I will make the lip and pads deeper to move the door forward.

I cannot use the latches commonly available at the hardware store or big box store as these almost all require 1 1/2" to 2" inches to mount. My thinking now is a simple pull handle on the outside, and a push plate inside.

I am thinking to use a magnetic catch, a bullet catch or the latch listed below. I may hold off on the catch after I see how firmly the screen door hinges hold the door closed.

If anyone has latch/catch ideas, I am all ears!

Here is a link that might be useful: latch

I need help. We had a double patio french door with vented sidelite installed by as it turns out a worthless door contractor. He did not order the screens for the sidelites. He is refusing to help us. We can order the screens from Lowe’s but we need the tracking In order to install them. Who or where can we get custom tracking made for our sidelite screens?