Sounds like you've made great progress
Personally for me, I like the whip to be my form of defence, so to speak. Don't need to freak the horse out with it, but if the horse gets too close, I can send it out, send it forward, use it to help stop. If I free lunge and a horse charges, I can use it to send the horse away (Whilst running around screaming.. happened last christmas with a stallion!! Let it off, and it just charged me!) and therefor, if anything were to happen, I has a whip :)
For stopping, you need to be assertive. Not aggressive, that when a horse will back up, hop up, or spin around to get away. Again, make sure you have whip in hand, and pointed to the bum to try and prevent any turning. I ask, Waaallkkkk and take a step forwards towards the horse, but infront of where the horse is going.. you get what I mean? That way, if the horse doesn't, I can position myself infront of the horse, not directly, that would be silly lol, but enough to block the path. This is another good reason to have the lunge whip as they're less likely to barge past you.
Duffy had some REAL bad manners, would do her own thing, and when I asked her to do my things, she'd go up, flash pretty hooves at me, spin, and gallop off as fast as possible in the other direction! Long lunge whip against her butt twice sorted that out.
If she doesn't listen the first time, I give the lunge line a good ol tug, which is why using a headcollar is good for green horses, I've never used a cavesson before so can't comment on them :)