I would lean toward tearing out the gas unit, and install stove in the living room. That is where you most likely spend your time in the winter anyway, you will not loose much floor space, and I'll bet that it will not cost a whole lot more by the time you figure in the cost of tile in the Florida room. I could be convinced though that you might spend more time in that Florida room in the winter, if it had a wood stove, tv, and recliner in there (and I would keep the carpet in there, to keep my feet warmer).