Setting up a proxy on a remote server

Okay, so first of all: Apache is the wrong tool!

Apache is a webserver, not a proxy server. Yes, it comes with a proxy module, but first and foremost it's a webserver.

Rather, you should look into a real proxy server like squid. And within squid you are looking for a feature called "Content Adaptation":

http://wiki.squid-cache.org/SquidFaq/ContentAdaptation

Ok, I figured it out.

I ended up with:

server {
    listen 80;
    listen 443 ssl;
    server_name proxy.example.com;

    charset utf-8;

    location @error {
        return 404;
    }

    location / {
        # only allow GET requests
        if ($request_method != GET) {
            return 404;
        }

        # do not allow empty urls
        if ($arg_uri = "") {
            return 404;
        }

        # do not allow non-app request origin
        valid_referers none blocked *.example.com;
        if ($invalid_referer) {
            return 403;
        }

        resolver 8.8.8.8;
        proxy_intercept_errors on;
        proxy_pass $arg_uri;
        proxy_set_header X-Real-IP $remote_addr;
        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;

        error_page 500 = @error;
    }

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

    access_log off;
    error_log  /var/log/nginx/example.com-error.log error;

    sendfile off;

    client_max_body_size 100m;

    ssl_certificate     /etc/nginx/ssl/example.com.crt;
    ssl_certificate_key /etc/nginx/ssl/example.com.key;
}