Update: Here's the picture. I think it looks much better!
Original post: I had a little better luck today with the Pearl-Ex. Using one big image and using cotton swabs to dab on the pigment seem to have helped. There's still a little smudging, but I think I can live with that.
The site Splitcoaststampers helped me figure out how to use Pearl-Ex. Now I don't feel like I've wasted my money!