In NoFL St Aug could easily remain green and growing/spreading all winter if not hampered by rye. Rye works in sports fields, but not so much for the home owners. Sports fields are intensely managed for greening in the spring including special chemicals not available without special licenses.

Since you have already used a chemical fertilizer, the best thing you could do is use organic fertilizer. Are you already mowing at the mower's highest setting? And watering no more frequently than once every 3 weeks for these temps?

If you're looking for something to do, spend $25 at Logan Labs in Ohio for a soil test. It would be more of a sand test, but still there are salts in the sand/soil that you need to know about to balance the pH and other salts. 16-4-8 might not be the best numbers for a fertilizer. The Logan Labs test will tell you. Post the results here for lots more information.

12lbs per thousand square feet or 12lbs on the whole lawn?

12lbs per 1000sqft. If I calculated correctly, that should have applied 2lbs nitrogen per 1000sqft? It hasn't seemed to have done anything at all actually

I will add some alfalfa pellets as that's the only organic fertilizer I can find. I'll also do a soil test soon

How many times per week are you watering? and how long do you water?

I have not watered in a long time except after putting the fertilizer down. I water 1 inch when I do.