Even thought the moose population was quite small to begin with, I think they have really seen a drop in them in Yellowstone as well. When I was up there this summer one of the NPS biologist mentioned the drop and attibuted it to habitat changes due to the fires over a decade ago. I don't know much about moose habits, but apparently they migrate higher during the winter and live off of forage from I forget which kind of tree. The fires reportedly really cut back whatever tree it was.
It is awfully coincidental that elk and moose are dropping about the same time the wolf was put in. Obviously wolves and hunting have a role. Habitat changes (unless it is dramatic overgrazing) don't work that quickly. And that area hasn't seen anything but a gradual change in habitat conditions due to development, etc. I suspect the answer ought to be reductions in tags and wolves/bears. The wolf thing isn't going to happen for a long time though.
My guess is the wolves have had easy pickings on elk. The elk had over 100+ years to lose their fear of canines.
By the way, the NPS can't "butt out" nor can USFWS. They are both responsible for management of Yellowstone. Its much easier said than done, but if both agencies as well as the states would apply a little common sense, there ought to be enough room for bears, wolves, elk, moose, and hunting.
A little bit of allowable culling of predators on private land would probably be sufficient to control the wolf/bear populations. I don't think it will be allowed for the forseeable future because the agencies are afraid people would shoot every one they see. However, I'm afraid we'll see a truly big drop in elk/moose numbers in Greater Yellowstone before any action is taken other than reductions in tags available to hunters. This one is going to get a lot worse before it gets better.