Let's start by saying it's my experience that Togglers are EXACTLY what you want to use, compared to other means of attachment. I don't mean toggle bolts or any other product that is not exactly named "toggler" with that "R" there in the name.

But wait a minute: what's the load rating for a pulling force on drywall? And is that any better or worse than your proposed situation, where each start and each stop of the mount puts a twisting motion on the mounts?

Also there's the fact that when you drill those 1/2" holes in the drywall, you weaken the drywall.

Then there's how many holes are being made in the drywall. Each hole weakens the drywall.

Then there's the fact that starting and stopping a screen motor pulls on the drywall, which adds possible points of failure.

I'd look up a drywall manufacturer and quiz them about this. Over the years I have found that most manufacturers want to get accurate information out to people who are using their products.

Is the screen being held in place by, say, three bolts on each side? I'd want at least that.