It seemed no matter how much color I layered on or how much brushing I did, I could still see the grain of the paper. I was kind of at my wits end when I remembered something I had read once on Nicole Caulfield's blog.
I went searching for the blog post where she talked about how she did the black backgrounds. She uses Polychromos!

So I went back to try again with Polychromos and it worked! It's still not perfect, but it's much better.

In this second shot I've also darkened the colors in his face and hair and tried to blur that birdfeeder in the background some more.