Fortunately, CJDNS works for this use case as well. It is possible to use a "tunnel" to connect CJDNS nodes via an IPv4 virtual interface or to connect to a gateway to IPv4. This way, IPv4 software can connect both to other nodes and to the outside internet.
At the moment, I believe that this is only configurable through the UDP admin interface, but this is most definitely a feature that we'll build into Cirque.
To connect to other nodes, it uses either IP(v4 or v6) or Ethernet Frames. See: https://github.com/cjdelisle/cjdns#3-connect-your-node-to-yo...
I'm working on a Django Rest Framework frontend for it, Cirque: https://github.com/jMyles/cirque, which will make this easier to visualize.