Okay, now that I've gone on too long about Ironite and those issues, what can I do to offer up some help?
Ironite is not the answer to the problem. Ironite is only an answer to chlorosis in some soils. It doesn't sound like you have that problem. It just sounds like you have a weak soil and are on the path to renewing it. Beyond the Ironite reference, I really like the suggestion made by Billusa99. Humate, molasses, and foliar feeding with seaweed or Garrett juice are great! Just give it time.
Are there any differences between yours and your neighbor's lawns? I'm thinking of obvious grass species differences and shade, but there could be other differences that are not as obvious - like surface compaction; use of chemicals to kill fungus, bugs, weeds; previous flooding; history of mowing tall versus short; slope versus flat; or other chemicals/organics applied. If so, now would be a great time to tell us. The compost should resolve any of the above issues, but it might take a little longer.
If your grass is 2 inches tall and holding, does that mean you have not mowed it this year and it has completely stopped growing? If so, I would order up a soil test.
There is a place in Texas that tests soils and plants from all over the world. I would send it to them. They are called the Texas Plant and Soil Lab. Click here -> http://www.txplant-soillab.com/
<- to visit them. You could have a salt imbalance that would be invisible to the naked eye and to many soil testers, but the TPASL will find it for you and explain how to correct it. I've talked to the owner and really like what I heard. They cost a little more but they do more tests. To get the same tests at other labs would cost you even more because the other labs would have to special order the materials to do the "extra" testing. Contact them before you send in a sample and they'll guide you as to how to collect the sample.