What you need to do is look at your soil to determine what is needed since it is a good healthy soil that grows a strong and healthy turf. These simple soil tests may be of some help.
1) Soil test for organic matter. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains� too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.

Of course it is worth making the switch to organics. Not to boast, but if you didn't already think there might be an advantage, you wouldn't be posting the question, would you?
Centipede is a close relative of saint augustine. And both grasses thrive when allowed to grow long (over 4 inches), and are not mowed too short. Also, both prefer lots of water, preferably one inch or more per week. A lot depends on your soil. You don't state what kind of soil you have. If it is sandy, more fertilizer is needed, but fertilizer for an organic gardener can include compost, which is needed in a sandy soil, and will promote the life in your soil. Organics is all about improving the soil life. Short term, your fertilizer requirements should not vary much whether you use chemical fertiizers like you've been doing, or organic fertilizers. But chemical and organic fertilizers are hard to equate with each other because they are not the same. Chemical fertilizers are about NPK. Organic fertilizers aren't. So if I were you, stop using chemical fertilizers today, spread some compost around instead, and water it in. Mow your grass high, but water it at least 1 inch per week in the middle of summer if you are not getting any rain. After that, fertilizer can consist of protein based cattle feed (corn meal, soybean meal, alfalfa, cotttonseed meal, molasses...etc) Microbes in your lawn will digest the protein and convert it into nitrogen for your lawn. In addition you get trace minerals the chemical fertilizers don't have, and you don't get the salts the chemical fertilizers do have. Post back here at the first sign of problems

The majority of the corn, soybeans, cotton, and now alfalfa being grown in the USA are the genetically engineered ones made to be resistant to glyphoswate products and/or with the "Bacillus thuringiensis" bacteria in them and they have not been tested to determine if it is safe for human consumption. Whether it is acceptable for an organic gardner/farmer to use these products is unknown because we do not know if by using them we are spreading them further afield.
There is also a geneticially engineered grass seed out there that has already contaminated nearby stands of the same species of grass that the company that sells it is still, inviolation of USDA and EPA rulings, is still pedaling.

I do understand the benefits of organic fertilizers. My question pertained more to the low requirements of centipede. Centipede does not require much fertilizing at all. It may look similar to St. Augustine, but it should also never been allowed to get to 4 inches tall. Centipede is best mowed to 1.5 to 2 inches. Because of it's low fertilizer requirements, I did not know if it was even worth switching.

Kimmsr, what do you actually recommend? I can't find a post where you recommend anything other than NOT using GMO items. Let's say soil needs lots of organic material, which I can guaranteed you most people's soils do, what should we actually do about it? Is there anything left that is acceptable to a truly organic lawn carer?

Soup006, I don't know how to determine if it's "worth" switching or not. I guess it depends on how you define success. It doesn't cost much to try organic fertilization on all or part of the lawn. Give it a couple of months to show results and, if it doesn't seem "worth" it to you, switching back is as easy as buying a bag of Scott's and watering it in.

versstef1, good question. I've asked before and still don't know. While I appreciate the concern of genetically modified products, a warning does little good if no viable alternative is suggested.

What to use depends on where you are. Up here grass clippings mulch mowed back into the soil provide 1/2 of the Nitrogen turf grasses need annually and mulch mowing the tree leaves helps with more. The best thing you can do is make the soil into a good healthy soil, well endowed with organic matter, and that is all that is needed. One rare occassion I might apply a poultry manure based fertilizer, but I have not seen a good reason to apply any fertilizer several times a year. If I do feed the soil, other than the clippings and leaves, it is done in the fall. If a good, reliable soil test tells me I need to corect the soils pH that is done in the fall.
My grass grows fast enough, with adequate levels of water, that I need to mow every week and if i fertilized I would need to mow more often.

That's good info, thank you. I'm still hoping to get some help w/ my weeds on the other thread. I know you say mulch mowing and taking care of the soil is enough for good lawn and will crowd out weeds. I'm still waiting to find some time to get soil samples and get a test. Any general tips for Florida sandy soil?

Just the same as I do up here with my Lake Michigan beach sand soil. Add organic matter.