Greetings!
I struggled with screen solutions for many years. I decided I preferred the screens on the inside, because I didn't like the looks of them on the outside. I have metal around all of my windows in my current van, so magnets seemed like a good solution. I tried individual little magnets, but wasn't very happy with them. I switched to the self adhesive magnetic tape to insure a good seal all the way around. I used no-see-um screen, the finest weave available. These magnets worked beautifully, and I leave them up on my rear windows pretty much permanently, because they're almost invisible. It is easy to pull them up to access the pop out latches as well. The front window screens I remove while driving.
The only problem I've had is that the self adhesive part which holds the screen to the magnetic tape gave way after about a year. I tried various ways to reattach the screen to the magnetic tape, and finally tried the school kids type glue stick. It works beautifully, and lasts a very long time. If it does come loose, it is very easy to reapply a little. I have been very happy with them.
If you don't have metal around your windows, I would use a second magnetic strip around your windows for the screens to stick to. If the self adhesive doesn't hold, I would try the glue stick for that too.
Hope this helps, keep us posted!
Cheers!