> you could feasibly do it on paper

Have you done this? You know of anyone who have done this? I know in theory it's possible to do, but claiming it's "feasible" I'm not sure is accurate.

> broadcast through a remote node

Which requires you to connect to the remote node, again using the traditional TCP/IP stack.

> overlay network gateway through TOR, I2P

Yeah, that would mask your IP, but IP still required, meaning your anonymous on the IP level, just like I argued in my previous comment.