Dont remove the topsoil, dont compact the ground, don't remove that many trees, don't plant bermuda, bahia or any contractor grass. It sounds like its probably too late. Bring in topsoil, soil test, select grass type based on site and desired traits.

And supervise the final grading to make sure it is level

As long as you are supervising, if they show up with a skid steer or a bobcat type vehicle (short wheelbase with high center of gravity) instead of a real tractor with big wheels in the back and little ones in front with a box blade in the back; then point and laugh at them and try to humiliate them for not knowing how to do proper finish grading. Tell your GC you want it done right and to get another landscaper. Getting a perfectly level surface that drains properly is THE KEY ELEMENT to enjoying your lawn in the years to come.

When they seed, YOU buy the seed. Spend as much as you have left in your bank account to get seed that is perfectly weed free (0.00% weed and 0.00% other crop). They will go to Wal-Mart and get a contractor's mix. You don't want that. Skip on down through the messages here to find one I posted about a month ago on why you don't want to get cheap seed.

When they seed with YOUR seed, be sure they roll it down with a water fillable roller or equivalent. The seed needs to be in good contact with the surface of the soil (not buried) to sprout and take root. The soil allows the hard seed coating to remain moist longer. You will be watering at least twice a day for a short period just to get the seed to sprout. Seed heavily. As it gets later and later, less and less seed will sprout, so by putting more down, you will have more come up.

You don't need to fertilize with synthetics until you mow the grass for the second time. If you fertilize before that you don't have any roots for the fertilizer to work with. If you plan to use an organic program you can fertilize several weeks prior to seeding.