wrobert is the expert on this, but I THINK it is Florida law as to which races are partisan and which are not. It is my understanding that the only way to change that, for us, is to become a charter county.
I do remember that we selected BCC countywide, then we went to single-district. Then everyone screamed that it was unfair because we (District 5) didn't have a hand in selecting the other board members too, because one commissioner can't do anything by himself/herself. So we went back to countywide. I do not remember whether we voted on that or not; I'm sure we did.