Replying to myself...
I just noticed that the tail fin isn't fixed in place and moves pretty easily along the boom. I guess it was too far forward. I've moved it back and definitely have better stability now, but I still have a way to go before it's as good as Michael describes. It generally wants to fly backward and in a circle, which I can't seem to trim out. I'm wondering if a bit of weight on the front will help so I'll probably try that if I can find some putty.
EDIT: Think I found the problem. See this