Thanks for the ideas, y'all. I just a minute ago realized I'd been using Option 3 all along.
My router has hostnames in its local DNS for some of the things on my network. The router itself is router; my fileserver is ike, etc. I just realized that typing those into my browser set to use the SOCKS proxy should give me their login screens if DNS requests are being tunneled, and an error if not. Sure enough, typing "router" into Firefox gave me the login prompt for my router. When I uncheck the remote DNS box and type "router", I just get an error.
So now I know it's working.