Switching to a harsher bit may not help the stopping problem. You'd be better off working with her more, rather than switching bits right off. She may respond better to you if you're better with your seat than the other owner was. Don't let her trot with you until she stops well at a walk - and when she does stop, make her back up a few steps. It helps to reinforce that whoa means cease all forward motion, not just pause. Then progress to the trot, etc....
As far as what style of tom thumb - really, try working with her first. Even if you're soft, the harsher bit can screw them up if the other cues aren't very clear, and understood first.
When you're ready to move up to a tom thumb, the snaffle part of it should look the same as the one she's using, just with shanks on it.
Ask Often, Demand Nothing, and Reward Generously.