Success. Apparently the no-pin method works. Here’s the link, circle diagrams and all.
I’m still puzzled why the head piece was originally drawn with an extra seam allowance. I cut it without the added seam, and it appears to match correctly with the body piece to which I had added a seam. I guess I’ll find out when I try to put it all together.
Note, though, in my excitement to get the two opposing circles to work, I completely missed the part where I was supposed to catch one of the fins in the seam. Hopefully the poor thing won’t drown.