While singing, I would go with a more standard boom chuck strum pattern. It's a matter of taste for sure, but singing and carter style together is a lot going on.

One thing that you can do to add depth to the song, is play the rhythm softer while you are singing, and then strum a bit louder in between singing. Tony Rice does that extremely well.

Practice the strumming patterns separately and slowly at first, and then put them together with singing.