Equi, Stacy is someone special. What she acheives with her horse is magic to me. You can't copy what she does merely by buying her halter - but who knows, a halter she approves of might help you.
The halter is a simple but very important piece of equipment which enables you to communicate with your horse. It is not a bridle and bit and of course it doesn't work on the mouth but it will allow you to make contact with your horse. I have a favourite blue and white string training halter which I have had for over thirty years - I've got used to it and the way it works on the nose and, when necessary, on the poll. With a young horse I used to fit it underneath the bridle.
I've used very thin string halters in Spain which the SPanish trainer used to leave fitted all the time.
Halters are a personal thing which give your fingers purchase and subtle control over the horse's head. When used properly they are a communication aid.
In my tack room I have several halters all of different materials and designs.
I find sometimes that a halter which works with one horse, doesn't work so well with another. So I experiment. And that is what I suggest you do.
You must find out for yourself which halter suits the way you use it, and which halter suits the horse which you use it on/with.