Sorry, a screen doesn't make much sense to me.
At latitude 33S in all day sun, you need one layer of 50% shade-cloth in winter and add a second layer of 50% for the rest of the year.
That is a general statement, some Genera might need more, others a bit less.
Florida is something like 30N.

What are you growing in the back of the house now?

I have found that I get a lot less burning on my screened southern windows than my unscreened ones. I am pretty "bold" with providing lighting for my catts, dendros, and encyclias though so I am not sure that I am the best example to follow though.

There needs to be some numbers to back up the word screen.
The "numbers" required vary greatly depending on the season, the latitude and the climate.
I remember reading some posts ages and ages ago that lead me to try full sun mid-winter on a few Cattleyas.
BIG MIstake!
Then there is the micro-climate in the place(s) where you grow your orchids and the aspect of said place.
My conditions changed when the 30 metre lemon scented gum was removed last year after it was damaged in a gale, all my enclosures now need additional shade-cloth.

My Schom brysiana grows in full sun, large plant hangs out between the roses, and some the vandaceous and denro's are in the ground by the trees to fend for themselves. When they are out in the yard, there is some constant flow of air which may not be the the case in the patio, and also a little bit of protection from the surrounding plants and trees, not a lot though...You have to gradually expose them to sun, circulating wind always help.

I have a screen enclosure in Florida. I have a southern exposure although the house shades late afternoon sun. All my orchids got burned, some so severely they died. Some of my orchids moved from NY but had 6 months to adjust to the higher light before I put them in the screen porch. I learned quickly, the screen did nothing.

The bottom line the screening does not protect the plants from the Florida sun. Even your highest light orchids will be stressed by the constant sun. If you feel the leaves, they are hot, really hot.

I had shade cloth installed on the roof of the screen enclosure. It wasn't easy and I could only cover half the roof. All my orchids are under double shade cloth, my guess is about 40-50% block.

I only have Catts, some dends in that light. My other orchids are hanging under a dense shade tree outside the patio. Some of the hybrids cannot handle the stronger sun. You need to know what species your Catts came from. Don't assume all Catts can handle it. Same with dends.

See if you can get some shade cloth and attach it to the screen roof. It won't block the rising sun in the East, but my plants can handle that. Its the mid day and afternoon sun which is too hot.

Jane

Arthurm, you are right. Micro-clime is very important. When I grew my plants in a northern exposure, with very little overhang, it was as you describe- double canvas over them in the summer and one layer or none in the winter. (Don't know the percentages, It was just coarse canvas). When we moved into this house, with a deep patio and a southern exposure I learned a lesson much like Jane's. In the winter the sun was lower in the sky and therefore reached deeper under the overhand for a longer duration. Burned a lot of plants before I realized my mistake.

For now, I have the plants fairly close to the same place they were growing before. Just a little closer to the eastern side of the patio to catch that morning sun. So far (its been two days) I see no burning and the leaves have not felt hot to the touch.

I have a mix of the usual villains. Catts, Dends, Phals, and some Oncids. Been getting some Tolumnias lately too. I have been growing the Dends on the east side of the growing area and by late morning they did feel warm but, they never seemed to burn. I guess they were acclimated. I am hoping that since most of the plants are already acclimated to the area before the screen went up, they should be ok and might even take a little more. I think they would like a little more light than they were getting under the overhang. They have not really thrived since we moved to this house. I guess the Dends will be my primary guinnie pigs for light experiments. My fingers are crossed!

Hi.
You can get screen in several degrees of reflective properties as well as shade cloth. Have nevr used my "screen room" as such so while repairing the hurricane damage went with vinyl lattice and grow vines on the roof
actually provides too much shade . of course doesn't serve as a screen room lol Wish I'd left the hardware cloth and light screen in place as it's a haven for squirrels ,spiders snakes toads ,cats etc. etc lol