I think it might be useful to be able to non-uniformly scale the area of influence of the bone strength tool -like the layer resize tool- so the influence could be stretched more one way than the other. A mock up of what I mean is below. I wanted to have the bone affect all the way out the lip without the teeth. I know I can do it by selecting individual points but would be nice.
It may not give you as much control as the approach you describe, but what if you just made the bone longer? On frame 0, use the Translate Bone tool to drag the tip of the bone out towards the lips. Then go back and tweak the bone strength a little bit.