Did you go back to your old post
and look at the answers? Here is the one that I think is going to give you the best results. And for my two cents, I'd suggest using an old blanket rather than carpet - it's likely to snag more of the burrs.
Oh my. I've been reading many forums for 10 years and almost all the advice above runs contrary to the collected wisdom of the Internet. Some is good, though so lets pick out that.
The blanket to pick up the stickers is very good. Drag it across the stickers and comb them out onto some cardboard or paper to collect them and burn or trash them.
You cannot establish grass seed without water. It must be watered 3x to 4x per day for 15 minutes each time. Do that for 3 weeks or until you have what you believe to be 80% germination. You need to get that done NOW because the window for bermuda seed germination is closing. Bermuda needs HEAT to germinate, so when the summer heat breaks, you missed your chance.
Save your money on compost. Compost is nice but it is not a fertilizer. It is the single most expensive thing you can put on your lawn. Corn gluten meal is the single best thing you can put on your lawn but this year it is very expensive. It is fixin' to get a lot more expensive with the corn crop failures across the country. Second best thing you can put on your lawn is soybean meal. This year it is relatively cheap. It has a lot of advantages not the least of which is that it will flow easily through a drop spreader set wide open. With bermuda you could apply soybean meal at 40 pounds per 1,000 square feet every week and still not get enough. Bermuda LOVES the nitrogen from soy (or corn gluten). Since you are on a budget, use what you think you can afford. Ask for broken bags at the feed store. Another alternative fertilizer is alfalfa pellets (Purina Rabbit Chow). Any of these materials will put organic matter into your sand. Eventually it will become very dark to black in color as the organic matter accumulates. The sand will still be sand but you will have a lot of water retentive organic material in there helping you with your gardening. Compost costs about $70 per 1,000 square feet while soybean meal costs more like $4 per 1,000 square feet. You can apply a lot of valuable soy for the same price as compost.
Sticker burrs are a symptom of poor fertility. That is why they are so common in sand. The only thing you really needed to do in the first place was water and fertilize. Stickers cannot compete with grass in well kept soil. They really are easy to get rid of simply by watering and fertilizing.
Bermuda becomes most dense when mowed at 1 inch or lower. There are issues with most home owner bermuda when mowing lower than 1 inch so that is a practical minimum. In the hottest heat of summer you can let it get up to 1.5 inches. That means when it is 2 inches high, mow it back to 1.5.
After your new grass becomes established, back off on watering as was stated by the other poster. Bermuda can tolerate the absence of water for a long time, but not forever. It seems to work very well to water it deeply once a week in the summer. In your sand you might need to water every 4-5 days. Then in the winter water it every month as a minimum. The soil/sand and microbes need moisture to perform the miracles they do in the cooler months. When you water do it all at one time. Don't water every day for 10 minutes. That is where weeds come from. When you let the soil surface dry out between waterings, the weed seeds cannot germinate and take hold.
Since you rototilled the soil first, you can expect to find a bumpy surface developing over the next few years. That can be fixed in an established turf fairly easily. You might not want to do it yourself, but it is not a difficult thing for a couple of strapping youngsters.
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