Now, this is my plan of action
1. Rototill the existing lawn
2. Cover it up (~1000 ft^2) with tarp to kill the weeds (and whatever
else was growing with weeds) - ~2 weeks?
3. Put in some new top soil
4. Apply weed killer chemicals
5. Re-sod
6. Water
7. Water more

If you are going to put topsoil on top, there is no need to rototill. Save
yourself some work, and just cover the grass/weeds up with a tarp. Also, the
topsoil shouldn't have any weed seeds, and even if it does, the sod should
suffiently cover them up so they won't germinate. There shouldn't be any
reason to use chemical weedkillers. If you're worried about weeds sprouting
in the edges of the strips of sod, just use corn gluten meal (found at a
local feed store) to inhibit seed germination.