I think what you have there is a severe case of snow mold. Thatch is a layer that lies on top of the soil, it doesn't mat down individual blades as it appears in your yard. Snow mold generally doesn't kill your grass unless it affects your crowns, but it will delay spring green up. This fall, after your grass has stopped growing, it would be beneficial to cut your grass lower than usual, 1.5-2 inches. Grass that's left too long going into winter can trap moisture as it lays down, and provide a nice environment for snow mold to develop. It looks like your grass was left on the long side before the snowfalls. I would rake the grass to break up the matted blades, then give it a good mow a little shorter than usual, maybe 2-2.5 inches. Even though it's still cool in New England, I would probably water a bit more than needed to get the grass growing. I would discourage seeding, as spring seedings generally don't do all that well, and you might be surprised how well grass can come back from snow mold. If you don't see any results in 1-2 weeks, then you might want to think about seeding, but again, late summer/early fall is the best time.

Sounds like you are watching too many commercials to help you with your gardening. Here are the basics of lawn care: Water deeply and infrequently. Deeply means at least an hour in every zone, all at once. Infrequently means monthly during the cool months and no more than weekly during the hottest part of summer. If your grass looks dry before the month/week is up, water longer next time. Deep watering grows deep, drought resistant roots. Infrequent watering allows the top layer of soil to dry completely which kills off many shallow rooted weeds. Mulch mow at the highest setting on your mower (special exception for KBG - mow at 3 inches). Most grasses are the most dense when mowed tall. Bermuda, centipede, and bent grasses are the most dense when mowed at the lowest setting on your mower. Dense grass shades out weeds and uses less water when tall. Dense grass feeds the deep roots you're developing in 1 above. Fertilize regularly. I fertilize 4 times per year using organic fertilizer. Which fertilizer you use is much less important than numbers 1 and 2 above. When to aerate? Never needed if you follow 1,2 and 3 above. When to overseed? Not needed with KGB. Overseeding is a fescue problem. 20-0-0 is only appropriate if you have bermuda. Any other grass would require a soil test to determine a specific mix of fertilizer. Chances are whatever is on the shelf currently is okay to use. But don't apply after Memorial Day. If you do you are getting into the summer heat. Heat and chemical fertilizer are not good for the grass. The sprayer approach to fertilizing is not a good way to go. Grass needs fertilizer at a rate of pounds per 1,000 square feet. The sprayer can deliver micro-ounces per 1,000 square feet. You'll need a drop spreader or a broadcast spreader and large bags of fertilizer. Trimec is one of any number of 2,4-d type herbicides. Don't mix it with anything else, especially fertilizer. Herbicides work best when they are spot-sprayed on each weed. If you are doing the 1-2-3 above, you likely will never need herbicide. If you apply it, though, you should see the weed die in less than a week. If you don't see that, then it could be the herbicide was not designed for that particular weed. Trimec types of herbicides are used on weeds like dandelions and clover; not crabgrass and other grassy weeds. Relax. It is not hard to do this.

There are some relatively low growing grasses that are sometimes sold as lawns that don't need to be mowed, but I think they grow a little too high for most people to consider them acceptable unmowed. So I think you're always going to have the problem that if you don't keep it mowed, it's going to get too tall. For now, your best bet is to try to control the weeds. If they're everywhere, you can just blanket the lawn with a broadleaf weedkiller, but it may be too late in the season for that, depending on your daily high temperatures. I think you're supposed to apply that stuff only when the highs are below 85 (maybe 80, check the label). That would be the case whether you're doing it your self or hiring it done. If you can't kill the weeds now, you'll have to wait until the heat breaks, unless you want to kill everything (grass included) and start over. If you kill the weeds after the heat breaks, you need to wait a few weeks before seeding, so you'll be cutting down on the time available. Before you seed, cut the existing grass as low as possible to give the seed a chance to get tall enough to survive mowing before you cut the first time. If you want to kill it all and start over, you can spray glyphosate in late July, then water a couple of weeks to germinate any weed seeds and spray with glyphosate again 3 days before you seed. To get the best results, use a slit seeder or core aerate to expose more soil to the seeds. After you spread the seeds, you'll need to lightly water 3x a day until the seed is germinated (probably 3-4 weeks). Then gradually cut back on the frequency and increase the duration until you're watering once a week and applying about an inch at a time (adjusted for rain and soil conditions). If you can't water regularly enough and can't count on late summer/early fall rain to do it for you, you can try dormant seeding, where you put the seed down when it's too late to germinate and it will germinate as soon as conditions are right in the spring. That may be in February (I forget what NJ winters are like; I have to do it in November here or the lawn will be snow covered in spots when other areas should be germinating). If you're replacing the lawn, you may want to consider getting premium seeds and going for the showcase lawn. Here is a list of custom blends of premium KBG by state. If you're overseeding into your existing lawn, you'll want to match its color and growth, which will probably be more like a good seed blend or mix from the big box store.

Bermuda Is a Nitrogen(N) Hog. I wouldn't worry much about the P and K. Your soil Ph is slightly high, but within range for Bermuda. All this will balance out with an organic program. From your options I would choose either Soybean Meal or Blood Meal or a combo of both for your existing Bermuda grass. If you choose to use both just alternate them every 30-60days during the growing season. Yes Bermuda should be feed N only that often. Apply the SBM @ 10-20lbs per 1000sqft. Apply the Blood meal @ 5-10 lbs per 1000sqft. In the spring you could use Alfalfa Pellets @ 20lbs per 1000sqft. How large are these bare areas?