The following link has a list of companies that provide transportation service in Yellowstone:
I originally posted here to get help as many of the companies I called on this list only provide bus tours. I also called the Yellowstone Backcountry Office, and they recommended Back Country Sports (Jerry Funke). I have arranged a shuttle with him for my trip in September. At $200, it's the second most expensive cost of my trip behind airfare, but there doesn't seem to be a lot of alternatives.
I broached the hitch hiking option with my wife, but she shut that one down pretty quickly. Frankly, I'm happy that she wants to go hiking with me as it is a great experience to share, and it means I get out more often. The downside is that my pack gets a bit heavier and there's a few more expenses. Both are trades I'm willing to make.