When you say IVR, you mean you have a 3rd party IVR, right?
In my shop, I have a skillset called IVR. Calls come into PBX/Symposium, get skillset routed to IVR, then, the IVR transfers the caller to a Symposium acquired CDN. Symposium then routes the caller to an agent.
I can track IVR time vs. agent skillset time, or either individually.