Why do you have a centipede lawn? Is it because your local people tell you that you have a very acidic soil? Is it because you were looking for something easy to maintain in FULL SUN that requires no fertilizer and very little mowing? Because if it isn't a combination of those two reasons, you might have the wrong turfgrass.

If you have any shade at all, then you have the wrong grass.
If your soil pH is 6 or higher, then you have the wrong grass.
If you have been fertilizing or liming it, then you got the wrong care instructions.
If you have not been watering deeply about once every other week, then you got the wrong care instructions.

Any of these mistakes will result in thinning and leave you thinking that adding more seed will help.

What's the better option then? My soil is clay with PH ~6.5. Mostly sun, no fertilizer, no irrigation system. 1/4 of my yard has centipede growing very thick, this part of the yard looks great which makes me think it would work. But the other 3/4 the grass is quite sparse in. Lots of homes here have bermuda lawns but I despise them. Would love to have a fescue lawn just so weeds don't have free reign during the 6 months centipede is dormant but I believe I'm too far south even for that (middle Georgia area).

mosquito,
You need to buy a 10.00 lawn sprinkler at Walmart.
It will go back and forth, and it will water the lawn nicely.
Yea, you can seed centipede any time you want til the end of July. but you have to run your lawn sprinkler for both your seeds, and the exsisting grass.
water your seeded area for at least 2-3 weeks, so the seedlings won't dry out.
When you see the grass starting to turn a slightly grasy color, water the whole lawn.
Really water it, turn your sprinkler on and go in the house for a couple hours.
Centipede grass needs more water than Bermuda.
There you go, you will have a nice thick lawn.
Centipede is VERY aggresive, it climbs up my fence in the back, so, once it is established, you will love it!
10.00 sprinkler, at Walmart.