First I want to totally agree that hens and cherry tomatoes is a guaranteed combo for good times. Mine are a lot more competitive and get far more excited than your crew. Cherry tomato time at my place, and I grow them just for the chickens, is gonzo!
However, I've had two casualties from cherry tomatoes getting stuck in airways, one hen died from it, and just two weeks ago, I almost lost another. I was quick though when she went crazy from lack of oxygen and fell over. I ran to her, held her upright and massaged her crop, and it helped dislodge the obstruction. But one more minute and she would have died, too. I've since learned that there's a special "chicken Heimlich". Making sure you have plenty of room, lift the chicken by its feet, bringing it shoulder high, then swing it down between your legs, the centrifugal force will dislodge the obstruction. Just don't let the chicken hit anything when you do the swing.
Now, when I serve cherry tomatoes, I sit in the run with a knife and cutting board, cutting each tomato in half before tossing them.
But have you noticed how totally rank cherry tomato poo smells?