For some reason, I suspect the answer may be Armwood. Although they don't have a lot of State Titles, they have made the title game multiple times since the beginning of this century. And being district champions most years, would have more home playoff games than road ones.
Assuming Armwood is the correct answer, I have no idea who last beat them in the playoffs on their home field.
Upon reflection, I don't remember for sure, but Armwood and Booker T. Washington had many epic battles when they were in the south bracket of the same classification. They typically met in the semis and it is possible BTW may have one one of those at Armwood. It is not clear to me that the Wood has lost any playoff games at home in the past ten or more seasons on the field. But perhaps I am forgetting a game or two ...