The proxy shouldn't have anything to do with this and is actually password protected by htpasswd -- therefore probably not accessible directly via plex.tv as there are no authentication options when adding a server.
That said, the proxy creates port 31400 in addition to leaving the original port 32400. When using 31400, it simply looks as if we are accessing the server from localhost rather than a remote host. 32400 will continue to block you unless you tunnel, because it knows you are not on localhost.
Clearing the browser cache and/or using another browser to test are also good ways to ensure nothing is up. Also, if you have a mobile phone you can try checking plex.tv from your mobile data. This will help you understand if your problems are localized to your home network or if it affects all remote hosts.