Varnish + cPanel never works out well. The only existing Nginx plugins have many flaws as well.
Litespeed would be a good option for you. I'd absolutely get rid of WP Supercache. That thing is an evil mess.
LSCache for WP works really well, and there's a memory-based caching plugin I found that works really really well but I can't remember it's name right now
@KH-Jonathan Do you have any articles regarding performance comparison using Litespeed and LSCache on WP?
I have tried some of memcached plugin, but still no lucks. I hope you remember the plugin name..