I was not happy with the OEM screen door latch on my 2014 Fleet, so I replaced it with magnets. There are small but very powerful ones available these days.
Two round magnets hold the screen door to the main door and a single rectangular one holds the screen door to the frame. The round ones just screwed on. I had to modify the door frame and make an aluminum bracket for the other one. Each magnet came with a steel strike plate, which I had to use because everything is aluminum. I also had to add little aluminum handle pieces to both sides of the screen door. I got the magnets from McMaster-Carr.
This arrangement is very convenient: Just pull or push the screen door to open it. I can even push it open with my foot while going out. The attraction between the main door and screen door is stronger than between the screen and frame, so when the door is opened, the screen comes with it.
It probably won't solve your insect problem but, otherwise, magnets are the way to go.
- Bernard