Some I agree with, some I don't. That start date might be a bit late for Nebraska. Not sure of your first frost date, but I would probably shoot for Sept.1 as long as the nights aren't warm and humid. Days in the high seventies to low eighties, nights in the low sixties to high fifties are ideal with the humidity being low. I like to use a dethatcher, they do increase seed to soil contact. I don't know if they make ones that pick up all the stuff, but if you are overseeding then after you dethatch you should mow the grass anyway to about 1.5 inches, so you can use the bag attachment on your riding mower. I wouldn't apply compost on top of seeds unless it is very fine, and dry. No more than 1/4 inch. 1/8 is better. Your watering schedule is wrong. 20k square feet is a lot, but once per day isn't going to cut it. You really need to water 3x per day to keep the soil bed moist, not soaked however. If you can't do that and only once per day is feasible then you should do it later. In the morning the seed bed is probably moist from the morning dew. You probably should water when the seedbed is it's dryest, probably mid day. Hopefully that will carry you over till the dew period. It doesn't matter that the seeds performed well in the NTEPs as most seeds have the same germination percentage. The higher rated cultvars will look and perform better as adult grass.

I was going to recommend everything tiemco said
- water a little a few times a day so the seed never dries out.
- Gradually mow the lawn down until it is "almost scalped but not quite. Bag all clippings.
- Dethatch so u can see the soil, this will allow great oil to seed contact. Ive seen neighbors try and dethatch and they leave lots of debris on the soil and throw seed down hoping it will germinate - no chance. good luck.