Thanks everyone, for the very helpful tips on English paper-piecing and the kind comments about my project. I'm going to leave the inner ring of papers in for now, and only take them out if it starts to get difficult to handle.
I'm taking it with me on a camping trip this weekend, so depending on how much time I end up having to sit around and sew, I might get the next "ring" done. If I do, I'll update with a pic on Monday!
Jan