I also thought about mis-clicking. This could be solved with a small timeout (say 1 second) before the home button has the new behavior and brings you to the first screen.
Baking in a magic threshold seems to be a worse option. No matter where you set the threshold, it's going to sometimes feel like the 'screen 1' vs 'last home state' choice is random (and wrong).
However, Apple already does this in other cases. If you leave the Settings app and go right back in, you'll find it exactly the way you left it. If you wait (I'm not sure how long, could be hours), you'll start at the top of the app again.
