don't mean to rain on your parade, but the fact is that the Internet is indeed the largest mesh network even possible and to propose a 'supporting' network is almost ludicrous, because by definition, such a network would simply become an extension of the network. in fact, there is NO WAY that bitcoin itself could operate without the Internet....again, setting up a 'second' or 'supporting' Internet is not really technically correct way to see it, because by definition this 'extension' or 'supporting' network would simply be another part of the Internet.
anyway, you can't really create an 'internet' backup, and your question demonstrates you don't really know how the Internet works, or what it means. I'm just trying to help clarify so you don't waste years on a dream that is fruitless. The Internet is just that INTER-NET, it's not just one network, but literally millions or billions of nets all tied together, and even the BitCoin network is just another extension. amazing right, when you really stop to think about it.
Actually, it's pretty clear that you're the one who doesn't know how the internet works nor what a mesh network is.