My instincts say that the tree is pulling away nutrients from the soil before the grass gets it. I'm no arborist but it is my understanding the active root zone for a tree is about the same as its canopy (your drip line). For my money, I'd apply a pound of urea nitrogen on that area with the next milorganite as a test (or heck, this weekend if your of a mind). If that doesn't perk it up some, then a soil test would certainly be in order. If you mulch mow your leaves in the fall, its possible the soil Ph could be acidic in that area. Just MHO, I'm sure the experts will offer better advice.

While bermuda can be beautiful, it is a hassle to keep it looking nice. It is one of the few grasses that should be mowed at the mower's lowest setting. Partially due to that, it should be mowed twice a week during the summer to keep from scalping it every week. Bermuda also needs as much water as all the other lawns if you want it to be green. The idea that it needs less water depends on your tolerance for brown grass. When bermuda gets very dry it becomes dormant and turns brown. When St Augustine dries out completely, it dies. Thus you have to water St Aug to keep it alive but you could stop watering bermuda altogether and it would remain alive but brown. Bermuda also needs monthly doses of high nitrogen fertilizer to stay green. This is to say that you can have a bermuda lawn but if you are not willing to maintain it, it is going to look raggedy. It can also thin out and become a haven for weeds. Back in the 50s, before the modern herbicides became inexpensive, when you bought grass seed you got a mixture of a fescue, Kentucky bluegrass, rye, and even clover. The idea was that one of the grasses would dominate in almost any soil and you could have a green lawn with multiple species of plants. That approach is one you might consider. You are in the transition zone meaning that you would be able to grow almost any grass.

I think it's amazing this thread went on so long with no mention of St Augustine. UC Verde and all the other buffalo and prairie grasses are for full sun. Kikuyu is one of the most invasive imported pest plants short of kudzu. The others mentioned are ground covers that do not repair themselves. Dichondra will die annually from flea beetle. They wipe it out faster than you can diagnose it, but it returns from seed. Fescue, in my opinion should be formally outlawed in CA unless you live west of the 5 in San Diego and Orange counties and west of the 405 in LA. North of the 10 it can be grown on the west slopes of the coastal range, but not in the valleys. St Augustine is a real turf grass, unlike many of the alternates mentioned. It spreads to repair itself under the dog feet, is very shade tolerant, also sun tolerant, and it will crowd out other grasses when mowed at the mower's highest setting. St Aug comes as pieces of sod on a pallet. Cost is about a dollar per piece covering about 2 square feet. It spreads 10 to 15 feet per year in all directions, so if you don't cover the entire area at one time, it will take over and cover for you. St Aug takes as much water as any turf grass if you want it to remain green. If you stop watering it for more than a month, it might die completely, so it differs from other grasses in that regard. But I have revived it from beyond the grave at my my new residence in the Texas Hill Country. St Augustine is considered to be a water hog, but that is pure myth. All grasses need 1 inch of water, once a week, in the hottest heat of summer. This goes for the cool season grasses in the north and the warm season grasses in the south. In Phoenix both bermuda and St Augustine need 1 inch every 4-5 days, but in the rest of the country it only needs it once a week. This time of year in your area you should be watering 1 inch, all at once, every 2-3 weeks. The problem with fescue is it needs water 3x per week in the summer and that dries up your aquifers and lakes. Not sure why you think you have clay, but you likely don't. I don't recall any brick factories in your area, so I'm skeptical. After 12 years of moderating three lawn forums, fewer than 10 writers really had clay. Your soil might have clay like properties, but those can be fixed. Even real clay can be fixed, but you have to have a good soil test along with a good reading of the soil test before you can fix it. 9 times out of 10 people who think they have clay have no clay at all but they do have fine silt and a salt imbalance (calcium, sodium, magnesium, and potassium). You can't know what the problem is without the chemistry test. A secondary issue causing hard soil is allowing the soil to dry completely such that the beneficial microbes in the soil are depleted and unhealthy. That can be fixed by spraying the soil with any clear shampoo at a rate of 3 ounces per 1,000 square feet. Follow that with 1/2 to 1 inch of water and let it go for 3 weeks. At the same time feed the soil with an organic fertilizer like alfalfa pellets, corn meal, soybean meal, or even Milorganite. Compost and/or manure won't do the same thing as the fertilizer. The deep moisture creates a perfect environment for the microbes. The organic fertilizer feeds them. Hard soil is easy to fix. The best soil test in the US is from Logan Labs in Ohio. Yes, it's been tested against all the other labs. Get their $25 test and post the results on the Lawn Care forum and you'll get about $250 worth of free advice from people who know specifically what to apply, when, how much, how often, and where to get the stuff. If you want to see some alternate grasses in action, visit Descanso Gardens and the Huntington Library in Pasadena.

I hear you on the budgetary problems. Everything but feeding's currently on hold around here at the moment! You can skip the boron, copper, and zinc for the year if you need to. While the boron is impacting lawn quality, the copper and zinc were more rebalancing. Still, you can work without the boron for a bit. If you have to do just one application of the potassium sulfate, cut the others and do whatever one is convenient and affordable for you. If it's zero instead, it'll survive. Prioritizing the above, the calcium lime is the most important. Potassium is number two. Boron number three. Copper and zinc a very distant fourth and fifth. Delaying will slow down soil improvement, but that's not a problem--it just means the grass improves more slowly as well. There's nothing wrong with doing that. Pine trees: The needles actually end up near neutral, although high masses of them can smother grass. The problem with pine trees is two-fold. One, they suck up massive amounts of water and dry out the soil profile. Two, they secrete chemicals that depress out or kill other plants to eliminate competition (literal chemical warfare). Grasses rarely grow well underneath or very near pine trees when you combine the above with the increased shade from the tree itself. But with proper care, you can get the grass to flourish pretty close to the tree, just not under the canopy. Improving the soil means the grass does much better, outccompeting the weeds. It takes time, and some work, but eventually the number of invading weeds drops amazingly. They simply don't have the space to grow and can't compete with the established grasses.