Lots of stop signs are 36" and they for the most part are .080 and on one post.
I would use .125" aluminum and run VHB tape at the very edges of the 4"x4" - from the top of the sign to the bottom. Then a few dollops of silicone between those strips of tape - like every 6" or so. One bolt at the top, one at the bottom, washers behind the panel to match the thickness of the VHB tape. It won't go anywhere.