The grass is going to grow like crazy in the early spring regardless of whether you fertilize. Professional grass farmers use their spring application of fertilizer to carry the grass from the time after that initial flush of growth into the summer. In other words they apply after the grass growth slows down. Hence the Memorial Day suggestion by tiemco. Seeding in the spring is not helping matters. You are probably going to water much more frequently to get that seed to sprout. If you would get all your 'densifying' done in the fall, you would be in better shape in the spring. Is your lawn all fescue with no Kentucky bluegrass? KBG would not work much in the shade.

One more test you can do is drag your fingers though it like you are trying to comb it. See if you detect "runners" called stolons. If so, I'd be pretty confident that it is poa trivialis. It's unusual for it to be spread out in patches like you have, but that might occur if the lawn has been aerated or verticut/thatched. If it is triv, the only thing that has worked for me is to cut it out and patch with sod. Maybe others have a different diagnosis or better remedy.

In terms of excess moisture, I just poked around a bit this morning on my way to work and noticed that the soil in that area was very wet. I also noticed lots of little bugs flying around that area! Also should add that a couple mushrooms have popped up in other parts of the lawn. With that in mind, I'm thinking a fungus has attacked the KBG and is leaving the fescue plants alone (so far). If you are not watering like the following paragraph describes, you should go there gradually over the next month. Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.

I swear nobody around here has heard of core aerating. I want to move there! Far too many people here think it is a panacea and solution to hard soil. Instead of clinging to that crutch, try this. Spray shampoo at a rate of 100 cc per 100 square meters. Your English is so good I'm going to assume you're a Yank living overseas. That converts to 3 ounces per 1000 square feet. Then water 1/2 inch to 1 inch and give it 3 weeks for the magic to happen. Since you're already feeding with organics, it should work quickly. I think your soil test is going to provide the solution. I am often luke warm on soil tests unless you've done all the organic stuff and it didn't work. Something isn't right and I'm going to guess it is salt balance. It could be something worse like too much boron or copper in the soil. The soils in the upper desert of Southern California are too rich in boron to be a good place for plants. Those micro nutrients are good up to a point and then they become a poison. Waiting until May should be fine for fertilizing. Fertilizing early with organics should not have been a big problem. The way they work the microbes would have begun slowly converting the protein into plant food for the plants as needed. Do you reseed the thin areas every fall? If your climate is anything like western Washington, you might be able to seed in the spring and not get summer weeds. How warm does it get in the summer?