Amazingly there is coax wired between the structures, and so there's a new variety of "MoCA" bridges that will use coax like ethernet, without disrupting your TV or internet connection. It's like powerline networking, except using coax, and also except it's actually fast.
We got the Netgear MCAB1001, and it works better than you could believe. 5 minutes to set up, and then it's on.
Since the ethernet side of the Netgear is 100mbps, it appears to bottleneck there, but I'm seeing 12MB/sec over HTTP, and less than 3ms everywhere. It really just works.