Is that the lowest setting? If so then mow it again at that height on Monday. The idea is to train the grass to grow horizontally instead of vertically. By clipping off the vertical stems, the horizontal stems will fill in. If you leave it growing up high, the lower stems get no sunlight and won't produce any blades. Now that you know your watering number (20 minutes), did you go to once a week cold turkey? With bermuda you can often get away with that. The roots that are there will quickly start to reach down for the moisture deeper in the soil. Here is a picture of what it can look like when mowed very low... Note how dense it is.

I will add, the frequent use of the word "poison" in stone's narrative suggests a less than complete understanding of what the various materials actually are, and what they do. If a specific herbicide has been compounded in such a way as to interfere with one or more enzyme pathways within green, vascular plants, is that a poison? The word poison has an actual and specific meaning. In human terms, a poison is a material which, upon being consumed, causes immediate life-threatening reactions. So, are herbicides which are designed to interfere with one or more essential enzymatic pathways within green, vascular plants poisons? Not to you and me, and not to moss (non-vascular) and not to a mature tree trunk which the material has drifted onto (No green tissue exposure). It is indeed tiring to see the same simple-minded "chemicals are bad" kind of thinking here. So, what about plants which exude allelopathic materials from their root tips? Must they be banished so as not to be poisoning the environment? This is just way too beginner for me. And in support of TR's comments above, you, stone, are putting lots of words in our mouths here. No, you're not the only person on this forum-if you can believe it-that would first seek out the desirable plants in a scenario such as above, for saving before proceeding to do any other work. It must be hard to live your life, knowing as you do that everyone else is an idiot who doesn't know what they're doing. +oM

I doubt the back is sinking. Your feet may be sinking into the mole tunnels. You may have grubs. Grubs attract moles and also feed on grass roots so your yard grass doesn't do well as a result. I have had excellent luck using milky spore to control grubs, and Tomcat poison worms to control moles. Milky spore is expensive and takes several years to establish, and with a yard as big as yours, will take some doing. But first make sure you have grubs. They are sometimes called "wire worms" so google them and dig around in your lawn to see if you find them. The drainage is a whole other issue . . . could be a grading problem. The way your yard is sloped, water should run off of it, or at least it seems that way from the photo but difficult to tell for sure.

Okay before you add any soil, did the contractor grade your lot so that it drains away from the house toward a ditch or to a paved road? It is standard practice for builders to "take out all the good soil leaving poor subsoil." Everyone thinks that happens, but almost always the remaining soil is not that bad. Both the chemistry and biology can be corrected very easily. If you bring in new topsoil, then that new topsoil is going to have its own chemistry and biology issues. Usually the problem with poor soil is an imbalance of salts like calcium, potassium, sodium, and magnesium. You can't fix that with more soil, but you can with a soil test and some corrective chemicals. If you're going to end up fixing it anyway (with normal good gardening practices), then why not just start with what you have? So before you do anything do this: Send a soil sample to Logan Labs in Ohio (not to your local university or county extension service). For $25 Logan Labs will test the soil and email you a report that is incomprehensibly complicated. Post the results here and morpheuspa will read it and tell you what you need to add, when, why, how often, and where to get the stuff you need. That alone is worth $250 from professional soil analysts. While you're waiting for the results to come in (less than a week), you can go ahead and work on the soil biology. That's done with organic fertilizer. The modern organic contain ground up nuts, grains, beans, and seeds. It turns out you can buy those ingredients at any feed store. Morpheuspa likes soybean meal and Milorganite. He likes them because they are good materials and he can get them locally. I can't. I like corn meal, alfalfa pellets (rabbit chow), and corn gluten meal...because they are pretty good and I can get them locally. The application rate is 15 pounds per 1,000 square feet. You can apply any day of the year, or every day of the year, without fear of damaging anything. The idea is to improve the soil biology. In 3 weeks you'll see a difference in the plants and grasses growing where you applied. In fact, here's a picture...This pic shows the effect of alfalfa pellets. You can see the improved color, density, and growth after a month. If your soil seems to be hard even when it's moist, then you can spray it with a surfactant like any clear shampoo. App rate is 3 ounces per 1,000 square feet. I sprayed my soil in San Antonio back in 2012 and it still gets so soft after a rain that it's a little hard to walk on. These three things will cost you roughly $30 and change. They are easy to do, will tell you a lot about your situation, and will get you started in the right direction. Or you can do it the hard way. You can bring in more soil, ruin your existing drainage, flood your house, and still have soil that needs to be tested and biologically improved. Well, maybe that part about flooding the house is a little over dramatic, but it has happened, so yes, I'm just trying to scare you into doing it my way. I started moderating organic lawn care forums back in 2004, so I've read and absorbed a lot of material since then. You're benefiting, maybe, from problems I've seen and seen resolved. Best wishes to you, and I say that not to blow you off, but because I hope what you end up doing works well. I probably raised a lot of questions, so feel free to keep asking. Oh and I wanted to say +1 to yardtractor. You called it thatch so I picked up on that. You had dead grass and it needed to be raked up. That happened, so I retract my earlier nitpick about thatch.