I mentioned Dogwaffle in my initial post. I've played with the free version and a trial of a newer version per your suggestion, but I couldn't seem to find any simple way to create an animation with layers. The closest thing I could find was the alpha composite feature, but I kept running into error messages whenever I tried merging two BMP sequences. Dogwaffle is a nice program, but I don't think it's what I'm looking for in this particular case.

I'll try looking around on thebest3d.com to see if there's anything promising there. (And to answer your question, my sprites are definitely going to be considerably larger than 30 pixels across.)