I'm actually quite smug with this one - I'd seen a friend repair their house screens years ago. When I got hJ I noticed that there was a gap around the edge of the window trims. so i decided to test if I could use same approach as house screens, and it works!
It's fiddly to do (esp coz I don't wanna damage the paint work) but I basically get an oversized screen length, wedge 4 short bits of spline into the corners so it's flat (like making a canvas), then gently squidge/shove the spline all the way around the edges (using a large flat short handled screwdriver in a kinda rocking action) and scalpel off the excess screen. there are a few structural blocks so the spline isn't entirely invisible but it looks ok and works brilliantly :)