They sell a screen fabric called "sun screen" or "solar screen" that can block 70 to 90 of the sun's heat/light. I'd try replacing some of your existing screen before damaging your frame by screwing another type of shade cloth over it.

Here is a link that might be useful: http://www.qualitywindowscreen.com/store/solar-screen-material-rolls-c-160.html

I use 50% aluminized shade cloth for my orchids. It is light weight and has lasted several years so far. I bought two redi-made panels and hung them inside my enclosure using six eye bolts. Using truck driver's knots makes it easy to tighten when necessary.

Here is a link that might be useful: Shade cloth

I partially installed lexan 50% in areas for my orchids. I've used it for years and like it. You would need a carpenter to install it. Unless you are the carpenter. Good luck.

Thanks for the info. I'm certainly not a carpenter and need to figure out how to get it up on the roof of the lanai. There's no way to get up on the screen roof, so it appears it has to be hung underneath the screen.

I have no idea who I could get to hang it. I bought a roll of shade cloth in HD but no one there could advise me.

Thanks,
Jane

The lexan can be installed above the screen. Not a DIY project.