Thanks for the information, guys. I have one of those setting tools and have been cutting them off about the same but my setting tool doesn't work all that well. It tends to bend the rivets over rather than mushroom them. Maybe I'll have to find a better made one. Or make one myself if I can't find a good quality setting tool. I made one to install the burrs for my #12 rivets and do have some good tool steel to make one from. Perhaps I'll have better luck with that.
If anyone has a good closeup photo of a properly set rivet, I'd be interested in seeing it.