I'm looking to play a Liverpool save next after I put down my Schalke save. I'm already planning on playing Carroll as a poacher. I'm also going to train him individually on quickness. He is good off the ball, has good anticipation, and determination. He lacks creativity, but that doesn't matter to a poacher. Playing him as a poacher would ensure he's always around the goal. It's the same way I play Huntelaar. He get's his fair share of goals off headers.
Also it depends on your team tactics. He could very well be simply holding the ball and bringing in other players. I imagine you want people putting crosses into him, not holding up the ball, if so I suggest increasing the frequency of crosses by your wide players.
Have you gone into the team tactics and set your primary target man to your striker? You can do that and still play Carroll as a poacher, advanced forward, etc. I'm planning on playing him as a poacher, setting him as the primary target man, and changing target man supply to "head".