Ken1538,
Sounds like you have given this a lot of thought and effort. That’s a good thing. However, Jessica may not be the best person to build your social skills with—she may just have issues of her own. Maybe you remind her of someone…who knows?
So other than not trying to engage much with her—you could take the direct approach, and sometime when it’s just you two say, “I feel our conversations are strained sometimes. Am I doing something to make you uncomfortable?” If she has an answer, great==you can work on it. If she doesn’t perhaps she doesn’t know or cannot say—either way—again, she’s not the girl to learn social skills on. Not everyone is—there will be folks that you click with and folks you don’t—you’ve given it lots of effort and thought. It may be time to just hand it up.