I used to do a fair amount of large Gatorfoam signs for stage backdrops. Sometimes they were mounted on stand-up panels, often they were hanging from wire. Many involved multiple seams, especially if they were 30 or 40 feet long.
I never used anything thinner than 3/4-inch Gatorfoam and I often made a lightweight wood frame for the back, especially the hanging ones. I wanted them to stay flat with no bowing or sagging. These were always painted, sometimes with cutouts adhered to the face. This was before digital prints.
Instead of making butt seams, cut the mating edges at an angle, just like the scarf joints on a long run of wood trim in a house. This allows you to get good looking seams, sometimes virtually invisible. The back frame keeps the sign from bending, which prevents the seam from trying to open. I also would sometimes glue a Gatorfoam scab on the back side right behind the seam if I wanted to absolutely guarantee that the two mating pieces stayed flush with each other.
Often, though, the organizations I made these displays for wanted to be able to disassemble them for easy transport in a van, so they needed to break down into 8-foot lengths. I still used scarfed joints for the Gatorfoam, though, so that, when the signs were reassembled, the seams were less conspicuous than a butt seam.
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Gatorfoam is an amazing material, though it's not cheap. I worked for a shop for a couple of years that actually cut letters out of it that were installed outside. The edges were primed with three coats of latex and then sprayed with acrylic enamel automotive paint, front and back. They were then glued to walls with silicone. The letters stayed flat and would hold up for a couple of years in the weather. They didn't look cheap and you would never know they were foam from just looking at them.
Brad in Kansas City