Again, it is important to understand that modifications must be made to my wooden model.
If you look at the width of the widest blade in the screencaps, to me at least, it appears as though this would fit inside the gauntlet housing.
Study my model. It is obvious that the base piece can be AT LEAST half as wide as it is.
Also, as per my explanation in my previous post, when made of metal and thinner, the blades would have a slight upturn on their facing edge. They would, in closing, pass over the pivot point of the one next to them(this point being the four right ones in my pic). The closing needn't actually stop until both parallel bars close on each other. This should illustrate that the housing need only be SLIGHTLY wider than the widest part of the widest blade.
If calculated properly and adjusted in design, the finished piece would fold into an entire package as wide as the widest blade.