Im going to suggest barefoot. I have 2 tb's and 1 of them has been having barefoot trims for about 12 months now. The other has not long started.
The first mare had very typically bad tb feet. That coupled with poor shoeing and diet made them really flat, dry and brittle. After about 6 months of barefoot I noticed her not stepping so lightly over stones or the road etc on the next farrier visit he said she had at least 4mm between her sole and the ground. Since then its become even better.
My 26 year old standie also has then sturdiest feet you will ever see and he has been barefoot for 10 years now.
If your horse is sensitive you can buy old macs or some other rubber boot to use for riding. I would also suggest you continue with the supplement and maybe look at the rest of her diet. Diet has a huge impact on their feet.
Unless there is some extreme situation where the horse NEEDS shoes then that is one thing but in general barefoot is much better for the hoof. It allows it to grow naturally rather than being shaped to the shape of the shoe which is obviously unnatural considering the front feet should be more round in shape and the back feet more oval not all 4 feet oval. Anyways I could go on for days lol my suggestion would be to go barefoot, check her diet and buy some rubber boots/shoes for times when the terrain is too hard or rocky. Eventually you will be able to ditch the boots unless going on a rocky trail or something.