From a Farriers standpoint, the vet said put shoes on your horse then it still didn’t get done. It sounds to me that the thrush issue is simply the horses hoof genetics. Not sure why the farrier wouldn’t do what the vet said in the first place, that is kind of rule one. They do have a higher education. I have shod horses in 5 states and the worst states for thrush are the dryer states with softer ground. Florida is bad even thou its a wet state because the ground is very soft everywhere. This causes hoof contraction which causes the Commissure too deepen and the heels to contract which in turn causes thrush in the frog cleft as well.
Every time I hear the words Barefoot Trimmer I get scared. There is no model for hoof trimming, shoeing and alignment. Its all genetics and you work to make the horse what it is going to be and correct defects that humans have caused due to selective breeding.
If you farrier is not comfortable shoeing your horse like the vet wants then it may be time to locate a different Farrier. Some horses need shoes plan and simple. Being a Farrier I have one mare that does and one that doesn’t. It just happens. I do not have a Thrush issue at all. Both horses have beautiful conformation just one is tender footed and thin walled. Thanks to human intervention for making horses “pretty” and not hearty.