You are correct in that I want /logs/ to redirect to a different site. However, a reverse proxy provides one benefit that simple redirection does not: I want to hide the location (port) of the site being redirected to. I want to be able to access the service on the 8000 port without opening that port to the web. A reverse proxy makes this possible.
I am willing to go through the giant pain of ditching my nginx setup and starting over with apache if someone can first tell me how to use apache to setup a reverse proxy alongside a wordpress install.