And those are exactly the ones where prequels are most intensely craved among the fans -- and which bring the greater danger. Leaving aside disappointing fans who wanted it to go the other way, there is the aesthetic problem of stripping the mystery away. There was, after all, the reason why you put in there in the first place. (Or so I hope.) It can add a tragic doubt and uncertainty to the characters' surroundings, and so make all their choices that much more difficult.
The first problem is making the resolution of the mystery as dramatic -- no, more dramatic, than the mystery itself. A common problem with books, but here, the mystery has had more time to build and take on significance.
And the resolution at the end of the book doesn't have quite the potential to cast a retrospective light on the events of the books that came chronologically after. If Prince John really was the heir, it makes Princess Jane's followers' noble attempts to put her on the throne look less noble, that you know they were suckered by a con.