How do I dynamically reposition part of a sentence based on the width of a word in the middle of the sentence that will change?
I think you could achieve this just by key-framing the Source Text control in your text layer.
Unless you have hundreds of them and need to do it programatically, I would just keyframe the changes of text, and the repositioning would happen automatically. 
If I have misunderstood what you mean, please add some screen shots to explain what you need.