I think it would have been better for Gary to back door Emmet while releasing the information that Emmet told him to put Liza and Tom up. Emmet is running the house and the only one that seems to realize it is Liza. They would also have the votes to take Emmet out in a clean sweep besides Jill's vote. And Gary would have a strong player gone while having the support of Tom and Liza on his side.