Since the new plan seems to be doing all your gating via code now, why not make the gates variable in what they are, use addressable LED's to indicate what mode each gate section is in and a key matrix to select what mode each of the gates is in,
Yes it may be a little advanced for younger kids but you could make it so it advances with them, if this unit is going to be designed as an educational tool for schools giving it the ability to teach the basics from a young age with the gates locked to a little older where they can select the type they think they need to a point where you can teach them that NAND's can make any other gate (although you'll need stacking connectors or bus bars, sorry Karen)
This could also work in the puzzle aspect of the unit in that you have to choose your gate or several gates, but you have a full range to choose from.