This is actually a cool idea and an example of thinking outside the box. You run a Tor proxy (bind to 127.0.0.1:9050) on a server on the Internet, and then run

This is actually a cool idea and an example of thinking outside the box. You run a Tor proxy (bind to 127.0.0.1:9050) on a server on the Internet, and then run a Tor hidden service inside your LAN. Then, you acquire an .onion domain for the hidden service (running inside LAN), and configure the Tor proxy (running on a server on the Internet) to access the hidden service via the .onion domain (for example, use Nginx to reverse proxy the hidden service). This should work. However, I imagine it could be quite a bit slower compare to "normal access", and requires extra steps to secure the transport connection between the hidden service and the proxy as you might not want to have everybody on Tor to be able to access that hidden service.