It also occurred to me that greyhounds are very prone to ehrlichiosis and babesiousis and that these conditions sometimes recur after infections at an earlier time in life. It might be worth looking for one of these. They are probably more likely than Lyme disease. I don't know the prevalence of Lyme disease in either NC or Florida but it is supposed to be less common South of the Mason-Dixon line, in general. The sores on the legs are really tough.
Antibiotic therapy helps some dogs, even when there is no obvious infection.
I recently attended a continuing education seminar on dermatology and that was also the experience of the speaker. In addition, pain relievers can be useful. It only works some of the time but it is easy to use. I hope that you do get some resolution of this problem, soon. Inc. Opinions expressed are those of Dr. Richards.