So I decided to paint it...the right way. Started with primer, let it cure, and then three coats of black paint. This project only cost $10 for paint. The most important parts of this kind of project are using primer to start and letting each coat of paint dry fully. I painted the knobs (that I had replaced a while back in an effort to update the piece) with a bronze glaze and it makes them pop. I also filled in the grooves on the front of the doors so the beadboard wasn't quite so noticeable.
Here's the before:
Black paint transforms just about anything!! It still has a bit of the country look it, but I think it looks so much better now.