The problem with "causing chaos" in general is that the game gets unplayable/frustrating fast. I think that, for some people, we already skirt that line. But right now "all" they have to manage is one Woe at a time, plus anticipate the next Woe, plus deal with the guys on the board. Any other abilities or tokens or whatever that they trigger are their own fault, and thus are expected. Oh, and there are the bandit keeps that pop up, but so long as you have a standing force those are at least quasi-routine (as compared to a catastrophic Woe or a god wandering the world at will, casting all sorts of insane powers).
Asking the player to handle a whole new source of completely-unpredictable chaos is, I think, one step too far. In other words, while it might make for an interesting option or an interesting super-high-level difficulty option or something, it's not a solution to the general issue you are raising, certainly not on lower difficulties.
I think that Mick brings up a really good point with the score gating rewards, though -- that alone would change a LOT.
Not that I don't also want to have some other unique challenges in the last age, but I don't think that "yet another layer of chaos," in whatever form, is the answer. It should be some sort of clear, concerted, concentrated challenge that players can see, react to, and deal with throughout the third age or a portion of that age. IMO.