Applying Card Art to Existing Footage (Planar Tracking in Mocha Pro)

I am trying to replace the card art on the attached clip. In Mocha Pro, the new AI matte tool does a really good job of tracking the card. Is there a way I can use that data for planar tracking? If not, what's the best way to make sure a planar track works correctly? I start running into trouble when the card tips forward (top edge moves toward the camera), and things get really bad when the bills obcure the card (I knew this would be a problem from the outset).

I've got the tools, I just lack the knowhow. Any help is appreciated!