Coming from an organic background, I would suggest you forget about your NPK and the ratios. I realize that is hard to do and you don't see anyone saying that (anywhere and rarely on this forum). Work on getting a grain type of protein onto the soil. If you want to fertilize with organics, get a plain brown bag of alfalfa pellets (rabbit chow) and apply at 20 pounds per 1,000 square feet. Cost will be about $12 for 50 pounds. Apply now and again in a month (since the soil has had nothing in 5 years). If you prefer you can use Milorganite, but I prefer alfalfa. When you do water, water deeply and don't plan to water for at least a week or when the grass shows signs of heat stress (blades folding together or a change in color). KBG would have been brown/tan all winter. Is that what you saw? If not then you likely have fescue.

i'm not going to watch the movie you made but i will say a couple of things. mice dont eat the wire, they eat the insulation off of the wire. even if they were to have chewed the wire in two, it's stil going to be the same wire color on each side of the break. there is a highly likely chance there is further damage that is concealed by engine shields, gas tank, etc.... if you don't know how to properly replace the damaged wiring then there is no sense in you researching the repair any further. (if that sounds harsh, sorry. thats just the way it is) good luck.

If you're going to overseed, spring is not the time to do it when you have that much go dormant in the heat. Depending on when you have your first frost, it may already be too late to do a fall seeding. You want to leave 6 weeks between seeding and the average first frost and I think that's already here for me (and it's still too hot to seed). The problem with spring seeding is that the grass doesn't really have a chance to establish before the summer heat kicks in. The problem with fall seeding here is that fall is too short. It seems to go from too hot to snow in a hurry. I've had my best results from dormant seeding. I wait until it's too cold for the seed to germinate and put the seed down (if possible, just before a good snowstorm hits). The snow melt and the freeze/thaw cycles will get the seed to the soil and it will germinate as soon as the soil warms up enough. There should be enough moisture from the snow melt that you won't have to water. However, I don't really think your lawn looks like it needs to be overseeded. I think you just need to get the grass to root more deeply. I don't usually core aerate, but I've been working on getting the organic content of my soil higher so that it will absorb water better (and the worms then take care of the aeration). If your organic content is really low, you may want to core aerate this fall (and maybe again in the spring if it's really bad). If you want to introduce some grasses into the lawn that will have a similar green period to the KBG but will need a lot less water, you can try adding some native grasses like streambank and western wheatgrass or some introduced grasses like crested wheatgrass. These are all cool season grasses that spread somewhat (but won't out compete the KBG where the KBG does well). They're not as dark green as KBG, but they don't need nearly as much water to stay green.

For leveling I would just add top soil to the barespots that need built up (making sure to compact it somewhat, I just walk over every square inch) and re-seed it at the same time. That's what I do for my tall fescue lawn. You need to get your watering cut down too, at best you only want to water 1-2 times a week max...long deep watering for those roots to grow downward and get established well. Just gradually start to increase your watering time (until it starts to pool or run-off) and start to skip watering days until you're at 1-2 times per week.