[nginx] How to serve all existing static files directly with NGINX, but proxy the rest to a backend server.

Try this:

location / {
    root /path/to/root;
    expires 30d;
    access_log off;
}

location ~* ^.*\.php$ {
    if (!-f $request_filename) {
        return 404;
    }
    proxy_set_header X-Real-IP  $remote_addr;
    proxy_set_header Host $host;
    proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
    proxy_pass http://127.0.0.1:8080;
}

Hopefully it works. Regular expressions have higher priority than plain strings, so all requests ending in .php should be forwared to Apache if only a corresponding .php file exists. Rest will be handled as static files. The actual algorithm of evaluating location is here.