My opinion...is that you should stay with slow release forms of nitrogen--that is make sure your fertilizer has at least 50 percent of the nitrogen coated to make it slow release. More than 50 percent if possible. Try to apply your fert during cool rainy periods or when rain is expected. April and May--September and October work well; try to get the applications 6 weeks apart. Summer is OK if during a rainy period. Grass should recover when rains start again. Compost will not substitute for water, nor for fertilizer. Kentucky bluegrass recovers from drought damage fairly well--it creeps to fill in thin spots. Perennial ryegrass (which is probably a high percentage of your lawn) recovers more slowly, as it does not creep. Reseed as needed about Sept first.
Photos seem to show many areas which do not have adequate irrigation water pressure. Discuss this with a top-quality irrigation company. Perhaps a well will work out better than city water--do you have a creek?
Meanwhile try to find a moisture meter to help judge how dry your soil has become, and compare areas. And learn how to detect wilted turf--and try to add water before the turf wilts, (for long) at least.
Sandy soil will gradually accumulate organic matter and become dark and more moisture retentative in a few years as the roots grow down into the soil and die.