Check our
About Our Homes | The Villages . It has basic floor plans for all home models in The Villages. Some of these plans are stretched when they are built so actual houses could be bigger or if you build a house you can stretch it. A quick check shows there are some Designer and Premiere models that meet your spec's.
The amount of space you are looking for is about right. The playing surface of a 4.5x9 pool table is less than 4.5x9.