Hi, and thank you for a great plugin.
I've created a patch for add_cacheaction so that you can send an array with class and function instead of just a function name, as it currently works in WordPress.
This enables plugin authors to hook into WP Super Cache with
add_cacheaction( "...", array( $this, 'function' ) );
I've done a quick search for more places where this change is needed and didn't find any, but perhaps the plugin author can make those changes if this seems like a reasonable change.