Am I on the right path with this girl who has very strict parents (10 points)?

Make every effort to spend time with her- without pressure. Perhaps the reason these other guys can't "get with her" is that they are pushing her too hard to make decisions about relationships. If you honestly do like her and can accept her and her family as they are, do your best to show it. If possible, spend time with her in group settings for a while, so that she sees that not only do you want to be with her, but also that when you are around other people, she is where your focus lies. Eventually, when you feel that the time is right for both of you to begin a relationship, you should make it clear to her that you are interested in spending time with her family. This will make it easier for everybody.