How to remove trailing slash from URL in nginx only if directory doesn't exist?

Question

I am running a server on nginx 1.4.1 with PHP-FastCGI. Currently I have it setup so that it removes trailing slashes from my URLs and issues a 301 redirect. However, when I visit a directory that exists, I am forced into a redirect loop. My current document root looks like this:

- index.php (app)
- webgrind
    - index.php
- static 
    - css

Currently I cannot visit example.com/webgrind or any other directory. My access logs repeatedly read similar to:

GET /webgrind/ HTTP/1.1" 301 178 "-"
GET /webgrind  HTTP/1.1" 301 178 "-"

This is the server block in my nginx.conf:

server {
        listen 80;
        server_name example.com;

        location / {
            try_files $uri $uri/ /index.php?$args;
            root /var/www/example/public;
            index  index.php index.html index.htm;
        }

        rewrite ^/(.*)/$ /$1 permanent;

        location = /favicon.ico {
            access_log     off;
            log_not_found  off;
        }

        location ~ \.php$ {
            try_files $uri $uri/ /index.php?$args;
            root /var/www/example/public;
            index index.php index.html index.htm;

            fastcgi_pass   unix:/var/run/php5-fpm.sock;
            fastcgi_index  index.php;
            fastcgi_param  SCRIPT_FILENAME  /var/www/example/public$fastcgi_script_name;
            fastcgi_param  APPLICATION_ENV testing;
            fastcgi_param  PATH /usr/bin:/bin:/usr/sbin:/sbin;
            fastcgi_intercept_errors on;
            include        fastcgi_params;
        }
    }

I am aware that rewrite ^/(.*)/$ /$1 permanent; is the offending line. If I remove it and visit example.com/webgrind, a 301 is issued for me to redirect to example.com/webgrind/ since it is a directory. However, my application will now accept both trailing and non-trailing slashes (i.e. example.com/users/ and example.com/users) and this is not what I want.

Wrapping the 'if' directive around my rewrite as follows still creates a redirect loop for my directories (if is evil, apparently, but a rewrite directive in this case is considered safe):

if (!-d $request_filename) {
    rewrite ^/(.*)/$ /$1 permanent;
}

(I know that visiting webgrind/index.php would solve my problem, but I'd like to avoid costly and unprofessional redirect loops when my production directories are pushed live.)

So how can I conditionally strip trailing slashes only for resources that don't exist (my web application paths)?

UPDATE: My (unaltered) fastcgi_params config:

fastcgi_param   QUERY_STRING            $query_string;
fastcgi_param   REQUEST_METHOD          $request_method;
fastcgi_param   CONTENT_TYPE            $content_type;
fastcgi_param   CONTENT_LENGTH          $content_length;

fastcgi_param   SCRIPT_FILENAME         $request_filename;
fastcgi_param   SCRIPT_NAME             $fastcgi_script_name;
fastcgi_param   REQUEST_URI             $request_uri;
fastcgi_param   DOCUMENT_URI            $document_uri;
fastcgi_param   DOCUMENT_ROOT           $document_root;
fastcgi_param   SERVER_PROTOCOL         $server_protocol;

fastcgi_param   GATEWAY_INTERFACE       CGI/1.1;
fastcgi_param   SERVER_SOFTWARE         nginx/$nginx_version;

fastcgi_param   REMOTE_ADDR             $remote_addr;
fastcgi_param   REMOTE_PORT             $remote_port;
fastcgi_param   SERVER_ADDR             $server_addr;
fastcgi_param   SERVER_PORT             $server_port;
fastcgi_param   SERVER_NAME             $server_name;

fastcgi_param   HTTPS                   $https;

# PHP only, required if PHP was built with --enable-force-cgi-redirect
fastcgi_param   REDIRECT_STATUS         200;

Answer 1

Putting the root directive outside of the location block as a direct child of the server block fixed the issue.

server {
    listen 80;
    server_name example.com;

    # This WORKS!
    root /var/www/example/public; 

    location / {
        try_files $uri $uri/ /index.php?$args;
        index  index.php index.html index.htm;
    }

    if (!-d $request_filename) {
        rewrite ^/(.*)/$ /$1 permanent;
    }

    location = /favicon.ico {
        access_log     off;
        log_not_found  off;
    }

    location ~ \.php$ {
        try_files $uri $uri/ /index.php?$args;
        index index.php index.html index.htm;

        fastcgi_pass   unix:/var/run/php5-fpm.sock;
        fastcgi_index  index.php;
        fastcgi_param  SCRIPT_FILENAME  /var/www/example/public$fastcgi_script_name;
        fastcgi_param  APPLICATION_ENV testing;
        fastcgi_param  PATH /usr/bin:/bin:/usr/sbin:/sbin;
        fastcgi_intercept_errors on;
        include        fastcgi_params;
    }
}

Apparently it is a pitfall that the Nginx wiki recommends to avoid.