Sure, nesting will work. Storing all your fixtures is the biggest head ache! You wouldn't need to automate the supports at all. I would have one base platform that could do all of the initial profiles for the top or bottom surfaces(if the beginning foam core blanks are near common size), then nest that finished side to cut the opposite side.
If I were to design it automated, I'd be looking at something addressable for up to 10 motors and plenty of I/O.
One option
If the center support could be stationary, you could have one screw for each end support horizontal position on one side of your base rail. Then one screw for each of the inner supports horizontal position on the other side of the base rail. Each vertical support could still use its own linear screw to adjust height and get clearance for flipping your part.
Then you could have stored position support programs(notepad .txt files) a PLC or a PC can send an RS-232 message for each motor controller to move. You would still need a seperate homing procedure on startup to reference the support structure.
Technically, you only need a rotary actuator on one end to flip it over, which could be handled by air to keep it simple.
Boards I have seen in the past were made with 2 part expandable foam. You could use the router to create molds and pour your own.....or use a finished board to make a mold for foam cores.
Lots of options.......if money is no object.
Al always comes up with cool solutions too.
DC