How is it that the Vale has so many houses going into debt? And is this only a phenomenon affecting the nobility of the Vale or could there be other forces at play here (eg. Littlefinger)?

I don’t think it’s Littlefinger, he’s more of an opportunist taking advantage of the situation than bringing it about. More, I think it has to do with the Vale’s obsession with honor culture demanding that the nobility keep up with the Joneses even if they can’t afford to, and the fact that unless you’re in the Vale proper, you’re likely to be ruling over marginal land with limited revenue.