In William Goldman's novel, Christopher Gill DOES kill Sarah Stone. At the risk of providing a spoiler, this causes Moe to "snap" somewhat. Suffice it to say that the ending of the novel is significantly different from the ending of the film!

I'd agree with thatshe just wasn't his type.
Actually, I don't think he had time. He didn't have the same element of surprise with Kate that he'd had with the older ladies. He had to catch her, and she was able to break away from him a couple of times. Monaghan and the boys were at the door, yelling to be let in just as he caught her, and it takes longer than you might think to strangle someone to death. You can choke them unconscious in one or two minutesbut it takes up to seven minutes to make them well and truly dead. And he needed time to get away. I think he just plain ran out of time.

Also, didn't he only kill middle-aged, matronly women?
"May I bone your kipper, Mademoiselle?"

Please keep in mind, I am only guessing. I think what stopped him from killing her, his relationship with Morris Brummel and he knew they were near by and did not want to be caught, dead center.