The only time I advocate tilling the soil is with new construction. But I'm not sure you can till Johnson grass to death. You'll always have JG seeds, so you need to get a grass in there that gives plenty of shade.
Before I go on, you ARE going to have a finish grader come in after the house is built to ensure the house is 4 inches above grade and no water can flow toward the house, right? I thought so.
When the finish grader comes in, you should time him with the landscaper. Oh, the landscaper is YOU! You should have the pallets of grass delivered while the grader is there and put them down immediately. And rent a roller to ensure the bottom of the sod is in good contact with the top of the soil. Roots won't grow through air gaps.
If you want compost in your soil, bring in 4 yards per 1,000 square feet and have the finish grader mix it in for you before you sod. If your current soil is basically rubble, have the finish grader haul away 6-8 inches of it and replace it with 6-8 inches of landscaper's mix.
Just so there's no confusion, after the sod is down, if you ever want to put compost on again, use no more than 1 cubic yard per 1,000 square feet. Otherwise you will likely smother the grass and kill it.
Dirt Doctor Lawns Forum