Here, I modified your list and added comments.
- Cut lawn to 1-1.5 inches
- Use Bluebird aerator to prepare lawn for seed (assuming aeration is needed)
- Dethatch entire lawn (power rake might be more appropriate depending on thatch layer if one exists)
- Remove the crap you just pulled up if it is excessive
- DO NOT REMOVE PLUGS? (no, the power raking/verti-mow will break them up)
- Seed with Black Beauty Ultra
- SHOULD I APPLY AT SEEDING RATE INSTEAD OF OVERSEED RATE? (absolutely)
- Spread Scotts Starter Fert over entire lawn (only if soil test shows it is needed)
- Topdress with compost if possible
- Water first thing morning then short blast mid afternoon to keep seed moist.
Temps here in Mass are about mid to high 60 in the day mid to low 40s at night.
IS THAT TOO MUCH WATER? (Yes. At those temps you should only need a slight irrigation around 1 PM. Couple of minutes with sprays, 5-10 minutes with rotors depending on distribution uniformity)