Without knowing why the grass is thin, since shade was not the issue, it's hard to say how fast the bermuda will return. It will spread in from the outside for certain, but there might be enough root structure remaining for it to simple spring up. You are watering too frequently. Your nursery guy sells plants, seed, and likely sod. The advice he's giving you will maximize his profits, not your enjoyment. When you water you should water very deeply without runoff. Deeply means 1 inch at a time all at once. Measure one inch by setting out empty cat food or tuna cans. Time how long it takes to fill the cans. That's your target for watering until forever. This time of year you should be watering deep about once every 2 weeks. When temps get into the 90s you can go to once per week. When temps get above 100 you should still be able to go once a week but you might see it drying out in 5 days. Then go to every 5 days until it cools off. You do not need any chemical type fertilizer until you have mowed the grass for the second time. Before that you would be wasting fertilizer when you have no active roots to take up the fertilizer. Then start a monthly program with any high nitrogen fertilizer.

Good thing you posted again. What happens with this forum is if you post a new message and leave it alone, it will remain at the top of the forum for several days while people decide whether they want to reply. What you did was immediately post more pictures. That released your message to drift down through the milieu of new posts right away. Your post today bumped it back to the top. You overseeded with bermuda on June 1 and less than a month later you are concerned about it not filling in. Is that correct? I would say, come back in a month and see if you have the same questions. How are you watering now? How often and for how long? It is time to fertilize with organic fertilizer. I would suggest using Milorganite as the bag rate. Milorganite is an organic that will not hurt your grass and will improve your soil. Typically centipede grasses thrive in the poorest of soils, so the Milorganite will be a good first step in reviving it. In August you can probably start in with the Bermuda Bible recommendations on fertilizer. With that soil you might want to alternate monthly feedings between organic and chemical for a year. All this fertilizer and water will kill off any vestiges of centipede you might have still hanging on.

There is no herbicide that will distinguish between common and Tif419 Bermuda. You're stuck with it forever. All of us are. Even if you could completely eradicate it in your lawn, someone somewhere is going to let his common Bermuda go to see and some of it will find its way to your lawn. The best we can do is to use cultural practices to encourage the Tif and discourage the common. The Tif thrives with lower cutting. You've already discovered that the common likes to grow taller. Hence, the reason for low mowing. When mowed low, the Tif gets very dense and thick. The common Bermuda is still there somewhere but it kind of gets lost in the thick Tif. A reel mower will allow you to mow down to a half inch or less. Yes, this is better but it would require you to mow every other day. I get the feeling that you wouldn't be too thrilled about the mowing frequency. Mowed at 1", the reel will give a superior cut and it will look better. As far as making the common Bermuda disappear, it's no better than cutting with your rotary. I think your main problem is the once a week cutting. As you've noticed, common Bermuda grows a lot more in a week's time than Tif. Double the mowing frequency and see what you think. I don't know exactly how old that sod is but I don't see the seams. If it were mine, I'd fertilize, water, and follow the Bermuda Bible. It's Bermuda and once established, you can't kill it, as you've discovered with the common Bermuda. Short of spraying RoundUp, you can't do anything to harm it that can't be fixed in a week or two. Feel free to experiment. That's half the fun of growing and maintaining a lawn.

Okay it's time to get much more serious. Have you looked for grubs? Dig up a square foot of soil and count how many grubs you see. You don't have to go too deep, because they feed on the roots. If you have more than a dozen grubs, then that WAS the problem. And since it is now almost September, the grubs have finished feeding for the season. You can kill them if you want to but that would be a waste of time and money. The places where they damaged the grass are already damaged and no more places are being added. It will appear that they are continuing to spread simply because the damage they do takes a few weeks to appear. The other bug to look for is chinch bugs. If you have those, they will be all over you when you're doing the digging for grubs. Check out this video for more information. I'm not worried about the amount of fertilizer you used. It's bermuda. If you can rule out bugs and disease, and when water and fertilizer can't revive it, it's time for a soil test. If you spend $25 on the Logan Labs soil test and post it back to this forum, it is very likely that morpheuspa will give you $250 worth of consultation based on the test results. Be sure to tell Logan Labs that you are having trouble growing bermuda. In the mean time you could apply corn meal at a rate of 20 pounds per 1,000 square feet. If it is a fungus, the corn meal should clear it out for you. Corn meal is an organic approach to curing turf disease.