What makes you think you NEED to spread winter rye? The benefits are it gives you a green stand of grass all winter, and something to do because you're going to have to mow it all winter, more than likely more than you did the St Augustine. Unless you're worried about erosion control in an area with no grass or just want something to do all winter, I wouldn't. You're going to have to water it, lightly fertilize, and take care of it. Now, given the option, me personally would overseed just because I'm a grass guy and went to school for it, but the average person I'd recommend not doing it. If you do decide you want a green lawn, go with perennial rye over annual rye, something like PhD, a triple mix perennial. The difference in perennial and annual is the perennial will be a darker, finer grass that also grows slower, it'll die off in the summer wth our heat so long as you're not watering 5 times a week.