After much searching, tweaking, and hair pulling I began to narrow the problem down to having overflow:hidden; on my menu.
I came across a few random posts of various sources that described a problem similar to mine, and there were always suggestions that it had something to do with the overflow property, but at first I didn't understand.
I was 'hiding' the menu by setting width:0;, so in order to hide the content as well, I had to set overflow:hidden;. If I commented that line out, the menu opened fluidly and consistently, but of course: I could see the menu items all the time. Not what I wanted.
I tried transition the display property to learn that you can't do that. So I tried the visibility property, and at first that didn't work either. However, I came across this post from a guy trying to transition the display property, and this answer happened to work for me.
I still don't understand exactly why this works, I think it has something to do with delaying the second transition so it doesn't stop the first... Here's the article he linked in his answer.
So I guess the problem really had something to do with Webkit and fixed/absolute elements with ul's in them... not repainting after certain... anchor tag clicks? Or transitions? Yeah, I still don't really understand. But it works now!