I am with dnovo...
A deer just mumbling along isn't a situation where I would think about stopping them. They will most likely pause at some point. As said, the deer on a mission through the woods or past my hunting spot is where it might be an option.
Also, I do not make use of a grunt. In my mind that is a sound another buck makes and the deer I want to stop may not want a confrontation. The few times I have made use of the "stop call" was in making a bleat. I associate this with a doe call and maybe it is less likely to cause the buck to bail at high speed.
I think it is essential to provide only one "stimulus". Making noise AND motion is a bad deal. Like many have said, probably best to be at full draw, have your spot picked out and basically "on go" when you try the stop call.
Just me... but I don't feel comfortable with trying to make a shot on a deer moving at anything more than a slow stroll. That's just me though.
OkKeith