The mixes sound fine to me, but I would actually ask the local Lesco guys because they deal with this over and over in your exact area. Your concept though is correct.
You should cut as low as you possibly can, down to 1" or so if possible.
You should continue to mow as you normally would and do your best to stay off the lawn anymore than necessary. You can mow a few weeks after seeding. An important key is to
make sure you do not mow wet grass or over wet soil, then you can tear and pull up the new seedlings. Since you have to water a lot to keep the new seedlings moist, the key is to not water one time so that it dries just a bit, mow, then water immediately afterwards to keep the water on the seedlings.
Lean on your local Lesco guys to give you the best advice on fertilization. Generally speaking a starter fert is used during seeding or overseeding, and formulations are also made for the fall and late fall/winterizing fertilizations.
Good luck, you got this just go to your local Lesco guys and trust they will steer you right. EVen if it sounds wrong, they know best, imo.