@Wille
Nginx reboots do not clear nginx’s fastcgi_cache. This was a surprise for me also when I was digging into it last year.
You can clean existing nginx cache by running rm -rf on folder where cache is stored.
I checked nginx config you have sent. It contains only server {} block. Outside it, somewhere, you will find a line like:
fastcgi_cache_path /var/run/nginx-cache levels=1:2 keys_zone=WORDPRESS:500m inactive=60m;
/var/run/nginx-cache is location where Nginx stores cache. As name implies nginx-helper only helps in caching & optimising. Nginx handles cache on its own using fastcgi_cache.
By the way, nginx-helper has a purge button like W3TC. That purge button can clean entire cache if nginx is complied with nginx-cache-purge module. Instructions for this are here - http://rtcamp.com/wordpress-nginx/tutorials/single-site/fastcgi-cache-with-purging/
Since you are already going with W3TC, try my config http://rtcamp.com/wordpress-nginx/tutorials/single-site/w3-total-cache/ here. It has some tweaks which most tutorials about W3TC do not cover.
The way my tutorial runs try_files is also appreciated on hackernews - https://news.ycombinator.com/item?id=4578856 
Apart from that some more tweaks…
For Line - https://gist.github.com/williejackson/defdbaba9c71572abc6e#file-gistfile1-txt-L41 , add log_not_found off; access_log off; in addition to expires max;. That will reduce disk I/O for static file requests logging.
Surround sitemap related rewrite rules in location ~ ([^/])sitemap(.).xml$ { } block. It will improve nginx’s response time by few miliseconds for every request.
For poll functionality, if its ajax, then you can still cache page but allow voting. I can’t explain more without analysing poll functionality, but since its a high traffic site, it will be good to add some extra rules. I did similar thing for a woocommerce based high traffic store and posted some magic rules here - http://rtcamp.com/wordpress-nginx/tutorials/wordpress/woocommerce/
Basically, we cached store pages also till a visitor clicks add-to-cart button for the first time. Cache store pages loaded fast and increased sales by few percentage! I think you can do some conditional caching for polls.
Since you are dealing with technical part, feel free to discuss. Nginx can do wonders and I will be happy to share my knowledge 
