There are a couple of us in currently in the midst of a bermuda reno. I started 6/1, the other guy started 6/15. If the initial cost of the sod is an issue, then just get as much sod as you can afford in lieu of the seed, peat moss, and other stuff you would have purchased. Cut the sod up into squares and plant those in the level soil every 12 inches (home made plugs). So maybe an August 1 st start considering lag time and unknown issues?

1. Soil test
2. Kill everything
3. Water
4. Kill again
5. Turn over soil/ rake - I would skip turning over the soil. It will create a weed problem and worsen your leveling.
6. Water - Not needed if soil not disturbed
7. Kill again - Not needed if soil not disturbed
8. Level/grade
9. Treat soil
10. Seed/pest moss / starter fert - I would lay sod. Seed is "cheaper" until you account for the 2-3 years it will take to fill in, the increased water, amendment, personal time/effort, etc. PM not needed.
11. Water
12. Hope for the best - Beer (Reeljake)

My steps would be:

Sprinkler repair/replace

Leveling

Sod instead of seed (we're not kidding!)

Water

Fertilizer

Enjoy

Turning over the soil would be the biggest mistake I see in there.

Tif 419 is the most popular sod in the south. Being the most popular makes it the least expensive, too. It will give you an instant lawn and save you a lot of frustration. Seeded bermuda will give you a common bermuda turf. The sod is a hybrid (actually a mutant) form of bermuda that is much nicer.

Another approach to getting a real nice bermuda turf is to buy a few pieces of sod, wash the soil off, chop up the remaining grass/roots/stolons, and scatter that over the area. They will take root and give you the same nice turf for a fraction of the cost (plus elbow grease). If you take this approach you could even buy the TIF Sport variety, which is normally 5x more expensive, but if you're only buying a few pieces, it will still put you in at much less than the seed will cost.

The single most important thing for bermuda is to get the perfect drainage and profile before you put down the sod or seed. If you turn this soil first you will hate yourself and maybe not even know it. The result would be a bumpy lawn that you cannot mow as low as you would like without scalping it.

Here's a motivational picture from the Wayback Machine...