Awesome job on getting the lawn into shape.
I'm goona butt in here with some advice. It took me three years to get my lawn growing consistently and to the point where I don't ever have to reseed. I got on a forum and chronicled my adventure. I had gotten a lot of great advice and we got it to do what 20 years of living here had not. I did it all organically. Last year I didn't have to add anything to it, and this year I just added organic fertilize in the spring. I will do that again in the fall. It is growing like gangbusters and all the spots that used to go bare don't anymore. Any areas that get torn up repair themselves. After a bit of work it becomes really easy to maintain. Almost effortless.
I believe you have sandy soil in Long Island, and therefore a lot of drainage. you need to get plenty of organic material into the soil. You can do this by top dressing with compost at a bout a half inch in the spring and fall. The most important part is to mow high. At least 2 1/2 to 3 inches. It will crowd out the weeds and I t is much healthier for the lawn to develop deep roots, which is what you want when it goes dormant in midsummer.
Here's the link that started me on the quest for a nice lawn. Probably more info than you wanted to know, but you understand how obsessive I can be by now. Believe me, this really works.
http://www.richsoil.com/lawn-care.jsp