I'm not an expert on these matters, far from it, but musing a bit here.....

A typical sliding patio door is 6 feet wide by 6 feet 8 inches high. Most of them come with a half-width screen, about 36" x 80" (2880 sq in). They don't have a mid-frame brace, and they seem to hold up to weather pretty well.

Of course patio doors are usually closed during windstorms, so I'd assume that has some effect on the wind loads the screens receive. Presumably yours won't be, and your screens will also be about 20% larger (3456 sq in). So maybe a challenge?

I think there are a few different keys to success here.

One is good, sturdy frames that resist twisting and hold the screen wire securely.

Another is a somewhat more open weave in the screen wire, to reduce wind loading.

The last is screen material that resists stretching.

There's a fiberglass screening with a slightly more open weave (18x14 rather than 18x16) and 18% larger diameter (0.013 rather than 0.011) that's intended for patio screen use. That would probably be the standard for a project like this.

Others here may disagree, but I'd be inclined to go for metal screening instead. Aluminum costs a bit more, and in my window-screen-fixing experience, it's worth it, though I've only compared it to standard fiberglass screening, not the patio screening I mentioned above.

The BMW of window screening is copper bronze, which costs several times as much as aluminum, but is very sturdy and might very well outlast you. In a given wire diameter, it's less likely to stretch (bronze's modulus of elasticity is 115 vs 70 for aluminum).

Going on the "if it's worth doing, it's worth overdoing" principle, why not go all the way to the Mercedes option? Stainless steel has an even higher modulus of elasticity (193) than bronze. I found stainless screen online in 12 mesh with a 0.023 wire diameter (twice that of standard window screen). It's far from cheap at $1,200 for a 4' x 100' roll, but you could probably knock down the house and still have the screens standing. (I exaggerate.) One potential downside is that screens made with this stuff would be quite heavy.

I'll be interested to see what others suggest.

Wire aside, and I agree with David the aluminum is more durable whike remaining cost effective. If you are using aluminum surrounds the size you are looking for will be too large. If you use extrusions the size of a patio door screen you can easily get 6' x 4' but then you will be looking at an awful lot of metal. Typical screen extrusions are 5/8" or 3/4" and honestly too small for a 6' wide screen.

I used the Screeneze system, which will allow openings up to 150 sf according to the manufacturer My biggest openings are about 5-1/2x12 ft, and the Screeneze easily supports that and stretched the screen nice and tight. It's been up for a couple of years through New England winters and storms with no issues, but we don't usually have hurricanes here. Even if the screens were to blow out in a storm they are almost trivial to replace relative to the old staples and lath systems I used to use. No need to have all the clutter of small openings.

I used to be a metal screen fan, but then found high strength fiberglass sold as "pet resistant" that I've come to prefer. We have one cat that won't be trained and though he claws at it he hasn't hurt it yet.

Thank you to all who replied to my screen dilemma...so appreciate the info, education and ideas!!! FP