The straight forward answer to your question is that JP can be one of the following
- Half Sibling
- Double First Cousin
The chart at the bottom of this page from the Shared CM Project will tell you more about the range of CM's seen for each category. If someone appears to be outside those ranges then the best thing to assume is that you have guessed the wrong relationship, not that the match is outside the observed range. There is a small chance that it could be outside the known ranges, but it is very much not the first thing you should assume.
I would suggest only using the match size as a rough guide to relationship. Unless it is a parent-child relationship it is always an ambiguous clue. To actually find out how JP is related to you, look more at her other matches. She is obviously related to you on your father's side. Does she have matches to cousins on your father's mother's side and to cousins on your father's fathers side. She might have a parent that is not related to you. If so she could have strong matches that are not in common with you. Use those to figure out who that non-related parent is and that might give geographical/time clues as to who the related parent is.