I can't seem to figure out how NOT to have the original post quoted when I'm posting a reply. Anyone know how to stop it?

Sure. There are two reply buttons, one is on individual posts, the other is at the bottom of the entire page. Click on the individual post button, and it will quote that post. Click on the reply button on the bottom and it won't quote.

Thanks. That's actually a handy feature, now that I know how it works.

Even if you just delete the quoted part, clicking on the individual post reply will also make the reply thread properly for users that opt for one of the two new display modes (threaded and hybrid).