From my understanding, if you have the premium version / service license, then you could contact via your site’s /wp-admin/admin.php?page=w3tc_support . This forum is mostly for free support, even though, the author of this plugin helps here at times.
These forums are only for free version support – so yes, do use the developer’s support channel for paid version support.
I just had a look at your site linked in your post. It does seem to be slow. There are multiple factors affect the speed of a site, and particularly the first byte time.
Btw, your site seems to be using “disk” for full page caching, as of this writing. Since, APC is already installed in your server, you may consider using it for full page caching as well. I hope that helps!
