I saw this news clip and was wondering if anyone has ever heard of this? http://metrosecuritygroup.com/newsclipsvideo_hi.htm
I live in Central FL (Lake Co), but I've never heard of this product. I watch the news clips, and the screens seem like a good idea for, as one of the clips says, large openings, like your lanai.
But I don't think these would work for all the windows simply because the hold-down eye hooks need to be in concrete. Also, because there is some "give" to the screens, I doubt you'd want them too close to the window, because debris could still push the screen into the window, which could break.
Around here, Storm Stoppers seem very popular.
Here is a link that might be useful: Storm Stoppers
Someone I work with had the Armor Screen you're talking about installed a few years ago here in South Florida. He's very pleased with it. He said there was a paper cup sitting on his patio table that didn't even move during Hurricane Wilma. You can see through it from the inside. That's about all I know. After Wilma I tried contacting a local company that installs it but I couldn't get a call back, but that was a very busy time here for the hurricane shutter industry.