I've seen APC a few times live and he's always using a rack with 2 axe fx units in it.
Makes sense for all the tone changes the guy does to just have it programmed
He used an Eventide Orville for the vast majority of the effects on that album. He also did some layering with Amp Farm. The base tone is the Naked Amp though.
He uses the Axe FX for his effects now. If he has the newer ones, it wouldn't surprise me if he "tone matched" his studio tone. Billy is heavily into programming.