So basically, you are bang-to-rights as you were too late paying. I'm assuming your PaybyPhone app doesn't allow you to back-time the time the parking is to start.
Anyway, submit informal reps against the PCN, based on your narrative. I think you should explain the circumstances and that you paid as soon as you were able to. Ask that they cancel the PCN on this ocasion as the circumstances were so unusual. Point out that you did not try to avoid payment, and only saw the PCN on the car when you returned to it later in the morning. You may get a result, but I can't see it worth risking the full PCN penalty at the adjudicators.