Some time ago I built some "Circuit Tiles" as I called, to teach something about electricity to my kids.
Searched the internet for some games, but found nothing available in my country, so I build some stuff with the thing I had.
Saw some games that had magnetic connections, some would clip, others had connections like puzzles...
My option was to interconnect the modules with alligator clips, using crimping terminals with a nail inside to secure them to the wood base tiles.
Since in your case, with a lot of connections to logic ports and such, I think an option could be use terminals like the Arduino boards has, and the connections would be made with jumper wires (like those used for breadboards).
EDIT: Why invert the type of connection you showed? Because you can even use simple wires with the insulation striped on the tips to make the connections, in case you run out of jumpers. And you could dedicate to each port, not just one interconnection pin/plug, but 2 or 3, since you may have to interconnect them with other inputs/outputs.Leave you with just some ideas...
I'm curious about your work, because I might be interested to move from electricity tiles, to electronic tiles. So your findings and options, may be useful to me.
