I'm no authority on southern type grasses so what I suggest comes more from seasonal visits to your State than anything else.
But....grass is grass, no matter where it grows and grass is not unlike any other plant....a lawn is just many plants growing together.

You say you have a sprinkler system and your lawn gets plenty of water. "Plenty". That envisions lots of what that word means. As far as the type...maybe St Aug likes more than other grasses but up north we go by the rule..generally accepted as sufficient....one inch per week whether by rain or hose.

You should understand that too much of anything is ..by definition...too much. Even a good thing.

Grass has roots and if given care to bring it about grass roots should be deep so they can stand up to what is thrown at them; drought, heat, shade, drowning, poor mowing, or no mowing.

I think St Augustine grass performs better when left to 3" to 4" high...shorter does allow more heat to penetrate into the soil and dries it out.

Too much water can bring about the same condition as too little...the roots gow short and makes the grass open to attack. Too little water does exactly the same thing.

Along with less moisture grass is subject to attack from pests and disease and loss of nutrition from not being fed.

You didn't say whether you have given your lawn any fertilizer, or if you do, when do give it. To green up a lawn sufficient nitrogen in the fertilizer will bring this about. To make it grow its best the other two elements...phosphurus and potash (potassium) along with the other minor elements encourages grass to grow and keep it healthy.

I noticed when I was in Florida this past winter practically every mention of fertilizer contained NO PHOSPHURUS in its contents of the bag.
Nitrogen, yes....potash, yes.....but no phosphurus or very little. The bags were listed as having 20/0/10....along those lines....
I suppose that says that Florida soils contain sufficient phosphurus and doesn't need any further help in that way.

Soils being what they are....one soil is not the same as the other. Plants use the elements in what soils they are given. To say one area doesn't need this or that...is suggesting the whole State has the same make-up.
Without a soil test, how is one to know. Phosphurus is vital for healthy roots and where it matters, rich blooming.

So one has to obtain better advice about the soil you have, in particular in your lawn, so that you can make informed decisions whether to give it phosphurus.

You can do a soil test yourself or send samples to a local laboratory....undoubtedly Florida State University has an extension service that does this or you can enquire about a private lab to have it done. Since you are new to the area I do suggest this be done.
Extension services by State funded colleges are listed in your telephone directory under "STATE" government or under the university itself. A phone call can quickly inform you whether the service is performed and how you go about delivering a sample.

I don't know for sure, but I once saw a TV show at a place called St. Augustine Country Club, so if you live in the country this may help. Mow your grass at 4 different heights. Longest on the ouside and shorter in the middle and shortest at one end. On the shortest grass dig a hole about 3" wide to let in water for the grass. Put a flagpole in the hole so the water knows where to go. On the next shortest grass, pull out a little bit of grass. Throw the grass into the air and look at it. If it blows away, it is probably too skinny and needs to eat so feed it, Texasweed or dchall will probably have better answers for you. Hope this helped