Hello Michael,
Thank you for reaching out and I am happy to assist you with this.
1. Yes, W3 Total Cache does work with IMH nginx reverse proxy caching.
2. IMH Nginx is controlled in cPanel, however, it cannot be purged via W3 Total Cache.
3. I am not familiar with the plugin you are referring to, so Ic can not suggest it for this use case.
This being said, if you want to purge the IMH Nginx proxy, you need to do this via the IMH Control panel
I’ve opened a Github issue for this and we may add the ability to do this via W3TC.
Thank you!