How to Use New Face Tracker to Stabilize Footage

I'm working on a project that needs to keep the actor's eyes in the exact same spot.  (The actor is facing the camera and keeping his head still as he performs, but there's still too much drifting of the eyes.)

I've tracked and stabilized footage before using the older tracking tools, but the problem I often run into is finding two spots on the face that don't move much to serve as reference points. (The actor has a very animated face when he performs.)

Can I use the new Face Tracking tools to make the task easier?  I'm not sure how I would take the tracking data and apply it to the footage in order to anchor the eyes solidly in one place.

Any help would be greatly appreciated!