I'd like to note that "the Internet" is a vast, broadly-scoped amalgamation of routers and different network topologies. They don't use one kind of hardware or software to manage it all. Any successor or parallel alternative network should be as (if not more) flexible to achieve it's goals.

I'd also like to suggest that the network be powered purely by standard Internet client machines and off-the-shelf hardware. Custom software would be necessary, but it's better to rely on a random guy with a quick installer on a USB key than custom hardware mesh routers deployed by professional installers.