Is there any way to created a screened-in balcony while still letting in lots of light for plants?
You could ... I almost did for my balcony. Instead I only 'screened' the perimeter using 60% shade cloth, tying to my wrought iron banister with nylon cording. But I could have easily not cut my shade cloth and attached the longer section directly to the roof over-hang for a more closed-in space. I like using the shade cloth because with a south-facing balcony on the second story that gets lots of wind too, I not only kept it a bit cooler but less windy as well, not to mention the added privacy. A much nicer habitat for plants and people, and my cats LOVE it out there!
The shade cloth can be cut and sewn together into any shape you like, so I could see tenting it using single rail at the top if you didn't have an over-hang. Shade cloth isn't excatly screen, but there is cloth screen that you could use as well, just more pricey.