Can you contact the author of W3TC (Unfortunately I think it is unlikely to work. I haven't tested it yet but my understanding of W3 Total Cache is that it requires the default Wordpress cookie to decide which cache to serve, and this cookie isn't provided by my plugin (we use the XenForo cookie instead).
I know him for while sometime and he is very active and helpful when it comes to his plugin. This W3TC is a really huge deal for many websites.