So today I finally was able to move the site to a new server build. I moved the site off of Amazon AWS because it was getting too pricey. The new server is built using Apache with FastCGI backend. Varnish offers a reverse proxy in front of Apache, which caches copies of the final HTML for the page, so Apache, PHP, and MySql doesn't have to be hit for every page load unless its necessary. Finally, Nginx stands in front of Varnish, which performs a bit better than Apache with large amounts of concurrent connections.
The results are pretty amazing so far. The server is handling the same volume of traffic on less resources and is performing way better. See the results in the graphs below.