French links act on the tongue, where single joints act more on the pallat.
So, a french link, when pulled, will drive down onto the bars and tongue, therefore making them want the drop their nose, and then, physically slowing.
I know we all probably sound like a broken record in saying this, but the bit shouldn't be what's stopping the horse. It's seat and leg. He's obviously not responsive enough, if he can't be ridden lightly in a simple snaffle. I know you said it's getting better, but I would keep him in a snaffle, and get down and dirty, and fix this no response to the halt cue issue. It can be fixed in a matter of one ride, if he's really believing what you say.
Full cheeks aid in directing, because of how the long sides act. It's why a lot of people like to use them with greenies.
Full cheeks are certainly legal in english disciplines. I'm not sure if there is any that it's not legal, since it's a snaffle...
Yes, horses get strong when they get excited, but that doesn't mean they're then allowed to lose all respect and not listen to you.
I'd put him in any kind of snaffle, french links I could see working nicer, and really fix the problems, to the point you'd even feel he's respectful enough to be ridden in a loose ring.