No piece of equipment can replace proper education, IMO you should concentrate on training Lucy instead of changing out her tack while riding her the same, and hoping that will get a different result.
I want to help, but I'm not sure I'm understanding the problem quite exactly - you say when walking or trotting she will listen and go at the speed and in the direction you want, but when you ask for a faster gait, she interprets that as "always gallop at top speed?" You say that even when she's galloping at top speed you can control her, but what does that mean exactly? If I'm interpreting your description right, she doesn't just bolt off, you can get her to stop when you want and turn in the direction you want, even at top speed - so what it sounds like to me is that she doesn't understand she's capable of going at a regular medium or slow canter, and you would like to be able to do that. Am I interpreting your question right?
If so, this is something she needs to be taught. No piece of equipment can do the teaching, you have to do this yourself, or find a trainer who can help you. This is one of the better horse-training problems to have! A horse like yours with a "go forward" mindset is usually easier to train than a lazy horse. The right trainer could fix this with just a few rides on your horse and then a few lessons with you, but if you don't have access to a good trainer or if it's not affordable, you might be a good enough rider to do it yourself. It sounds like you have good balance, maybe not a huge amount of knowledge but definitely some talent, a lot of bravery, and an attitude of enjoying your horse and a commitment to doing what's best for your Lucy. Add in a lot of patience, and you can possibly do it.
The snaffle bit you're currently using is fine - just make sure your bridle is adjusted so your bit rests on the bars of Lucy's mouth, on the gap between her front teeth and molars. It can slightly brush against her front teeth, but not go any more forward than that. You might need a noseband, just an average cavesson that's not attached to the bit in any way, just hanging from the poll part of the bridle, only tight enough (3 fingers) to make sure she can't open her mouth wide enough to get the bit between her molars.
The main thing you need to do first is teach her to go at different speeds in all gaits. Do you have a smaller area, like a round pen or arena to work her in? It would be helpful to start out in a smaller area where she can't work up to an all-out gallop, but it can be done even if all you have is a field, if you get her used to working slowly in the same small area every day.
Get her to do a slow walk, then switch to a fast walk, then a slow walk again. Praise her every time there's even a small improvement in regulating her different speeds at the walk. It might take several rides until she really understands that she needs to regulate her speed according to what you ask. Make sure you do this training in both directions. Then do the same at the trot. Slow, fast, slow. Fast, slow, fast, stop. Train yourself at the same time - your signals to her for the speed you want her to go, should come mostly from your seat and weight first, then your legs, and finally your hands will only be for fine-tuning to make her response more quick and accurate. For example, if she's trotting too fast, slow down your posting bit by bit until her pace matches yours.
Once she is responsive to different speeds at the walk and trot, try combining the two. Slow walk to slow trot to slow walk. Fast walk to fast trot to slow walk, fast trot to slow walk to stop, to slow trot, etc...You get the picture. Lots of transitions in the same gait, to and from different gaits, and stops. Only after she understands that you are in charge of her speed when you are riding her, then introduce the canter (lope). Start only with brief transitions, like trot, ask for canter, then ask for trot again after only a couple canter strides. Try this in both directions, on small circles and large circles, gradually work up to full circles at the canter. It takes a lot of fitness for most horses to do slower canter circles with a rider, different muscle strength than galloping at top speed, so ask for it gradually in between doing a lot of trot (cardio) work in between.
Once Lucy's fit enough to do slow, smooth transitions from walk or trot to slow canter, responsive to your weight and seat, then smoothly down again from canter to trot or walk, you will have an impeccably-trained beauty who can not only beat other horses in a race-only when you ask- but an awesome horse who understands and can do everything she's asked. Can I guess, she used to be a barrel or gaming horse? Just a guess.
Good luck to you,
Lucy sounds like an awesome horse!
