If you were going to do this "right," you would have waited until fall to do the seeding. And you would have waited until Memorial Day to fertilize. And you would have waited until after you had a good soil test to apply calcium, because the soil test would have told you whether you needed it at all and it would have told you how much to apply and it would have told you which of the two kinds of calcium to apply. And if you were doing this right you would not have applied top soil as a top dressing - now those areas will be permanently higher than the rest of the lawn which can cause them to dry out faster. But all that is water under the bridge. Let's look forward.

Your watering system is good but slightly off on timing. If you are trying to get new seed to sprout, you can reduce the time to 5 minutes, but keep it at 3x per day. The 20 minutes will give you soggy soil. All it needs to be is moist enough to sprout the seeds. Soggy soil for weeks can create a swamp culture of biology in your soil. When that happens you get weeds like nutgrass and other sedge plants that can be hard to get rid of. What you want is the normal prairie type biology in the soil. That requires a little moisture and a lot of air. Once your grass is completely sprouted (80% sprouted) you can start to back off on watering frequency. Eventually you will have it set to water once per week if your temps get into the 90s. With temps in the 80s you should be deep watering (1 full inch all at one time) every other week. You can time how long it takes your system to deliver 1 inch by setting out cat food or tuna cans in the yard. Turn on the sprinkler and time how long it takes to fill the cans. That will be your watering time from now on until you change something in your sprinkler system. Different sprinkler heads or different lengths or diameter of hose will give you a different time. Even kinks in the hose affect the time.

The problem with seeding this time of year is the crabgrass seed is waiting to get water 3x per day for 20 minutes per time. Crabgrass is an opportunistic plant that thrives in full sun summer conditions. It spreads faster than other plants, leaves a lot of seed behind, and then dies with the first frost. When you seed in the spring the likely outcome will be a nearly full crabgrass lawn by mid July. But don't get discouraged. In the fall, which is late August for you, you can kill off the crabgrass and reseed with the appropriate seed for your situation. Having crabgrass for one season is definitely not the end of the world. There are benefits to having roots in the ground no matter how noxious the weed. Next year you can have a really nice lawn, so you should not need to wait 2 years, unless you were counting next year as a full year. Next spring (April) it should be pretty nice.

Other thoughts:
Don't apply top soil as a top dressing for anything unless you have poor drainage or low spots you need to raise up.
Mechanical aeration is the old way to soften soil. Besides the fact that it doesn't work, it has been replaced with a couple applications of a surfactant like shampoo. Any clear shampoo, sprayed at a rate of 3 ounces per 1,000 square feet, once, twice, or three times at 2-week intervals, will do much more to soften your soil than aeration ever will. Total cost for you might be a few dollars if you buy your shampoo at the dollar store. You definitely don't need fancy shampoo to spray on your lawn. Just get any clear shampoo like baby shampoo.
Before you apply any more calcium, get a soil test from Logan Labs in Ohio and post the results here on this forum. Scan through this forum to see what kind of suggestions you get from morpheusepa.
Birds are generally a good thing in the garden. They eat damaging pests and leave behind one of the best organic fertilizers you can get. Some birds will eat your grass seed, but they can't eat enough to do you much harm. Think positively with birds.
The right time in your area to fertilize is late May. Since you already fertilized your grass will end up being stressed. It will struggle through the summer if you don't fertilize again. I would start using organic fertilizer to help relieve that stress from all sides. With chemical fertilizer you're always asking if I can apply again in 6 weeks or whatever. With organic fertilizer, you can reapply later that same day, the next day, next week, next month, and/or never (not recommended), but you cannot over apply (unless you smother the grass with 1/2-inch of fertilizer). So you never have to worry about that issue. And there is no interaction between chemical and organic fertilizers so you can apply chemical and organic the same day.
With your grass you should be mowing at or near the mower's highest setting. When your new seed gets up to 4 inches, you can mow. That may or may not be 6 weeks.
For your area in the front where the new grass is struggling, is shade an issue there?

Awesome, thanks for much for the help. This is my first home (we owned a condo previously but didn't deal with lawncare) so I'm definitely new to everything. I tried my best to follow Jonathan Green, Google, and other places but lots of conflicting information. Really happy I found this forum.

I knew Spring was sub-optimal but sort of wanted to get a head start so I didn't have to look at a dirt pit in the front yard all year. Lesson learned.

For the front and side, I think shade is definitely some of the issue. Overall, I feel like the seed is now just barely showing up in most places (exactly two weeks after) but I'd guess at less than 50% germination thus far. The sun rises in our backyard and sets in our front yard so I'm thinking the front of the house ultimately gets less sun overall.

It sounds like my best bet is to organically fertilize in May, cut back a bit on the water, get a soil test, and really try to seed come August? I figured I wouldn't have a great lawn until Fall of 2016 and willing to do the work. I guess I just didn't quite know what to do. :D

I'll try the baby shampoo trick. Does core aeration make sense when overseeding or did I waste a bunch of money buying a towable core aerator? :P

Again, thanks for your help. I *really* appreciate it.