This gives me an idea (I think it's pretty much the same as what Mitchell wanted):
(EDIT: Forgot to attach the image)
Bottom is the current bridge layout, top is the new one with CIWS on top. The bridge is extended to compensate for the space lost because of the CIWS. Don't know if I got the scale right. Anyways, space in the bridge isn't really reduced as drastically, it seems.
Why am I still pursueing this idea? Because this grants an angle of fire greater then 180 degrees. Considering the other CIWS has an angle this great too, this grants overlapping fire and eliminates any weak spots in the CIWS design. Plus because it is taller it can fire over the bow. Or so I think; correct me if I'm wrong. At least, this was the intention with the original Anghellis.
Below the bridge is the command structure; that can be extended as well, I suppose.
Leaves only a single thing that might be a problem, possibly; maintenence. I have no clue about that in this case.
Btw, Mitchel, to get a 360 degree arc of fire the CIWS would have to be at the highest point, on top of the tallest mast. I can see that would be a bit tricky for maintenence crews.