I have the same setup. My struts are very strong. I had to reattach the brackets inside with larger screws. I wouldn't worry unless the wind is really strong and knocking the door around.
Those extra pulls are a great idea vs the single tiny pull in the middle! I am very careful while opening or closing not to over stress the door. I can see where it could want to "fold" along the strut mounting points.
I sliced a bright green pool noodle to clip over the edge of the door when the site terrain dictates that the open door hangs lower than our noggins
