Thanks for explaining your thinking and continuing the conversation.
I think this is the problem with trying to diagnose training problems over an internet connection without seeing the actual horse. My impression of the horse based on the OP's description is very different than yours, and whose to say whose is correct?
If the horse is just simply lazy and lugs behind and makes you tow it when you lead it, then a chain shank under the chin can be part of the solution. With that horse, I'd also do some basic reschooling using a long wand or dressage whip and get it to walk on and stay up with me. I also sometimes used a chain under the chin as part of the rig when ponying another horse, in order to keep my arms the same length.
However, the OPs descripition of the horse really makes me believe that the horse is fearful. And therefore, I'd be reluctant to have her run backwards, hit the chain, even one under the chin, and convince herself that she was right to be terrified in the first place. So I'm inclined to agree with the posters that advised groundwork and reassurance.
The other piece that I will agree with you on, though, is that a horse like this needs a *confident* handler that communicates clearly that they're the alpha. If you give a fearful horse a nervous or timid handler, they quickly become convinced that there's a cougar behind every tree. A no-nonsense, zero tolerance "We're walking here now because I say so" might very well work; I just wouldn't add the chain.