Centipede Grass Eradication
The grass you are trying to eradicate is most likely bermuda grass.Because of the warm temperatures, it is still actively growing. Spraying now with a nonselective herbicide ,like Round up (Glyphosate) followed by slit seeding with a mixture of turf type tall fescues will help eradicate the weed. The attached publication will provide more detail in the process. http://extension.umd.edu/sites/default/files/_images/programs/hgic/Publications/non_HGIC_FS/TT%2046%.
I have done exactly the recommendation you have posted 2 years in a row, In fact I used multiple applications of total vegetation killer over a 3 week period, then hand raked out the visible traces of vegetation.
I also used a hand tilling tool to dig out most of the root system of the centipede grass; as many as I could find. Then sowed the new grass seed.
This did not totally eradicate the centipede grass. If even one small, undetected root segment of the plant remains, the Centipede grass will come back.
Again, I did this 2 years straight with the same results, a reemergence of the centipede grass.
Do you have any other recommendations?
Start the round up applications sooner and repeat for a second or third application. Allow the round up to work by not tilling the soil. Slitseed into the dead grass.
What month should I start this process.
If your approach does not work, do you have an alternate approach?
BTW, the past 2 attempts, I did apply total vegetation killer for 3 weeks (once per week), then waited 2 weeks before raking, tilling, and pulling roots.
Now is a fine time.
If you used a total vegetation killer containing the active ingredient glyphosate or triclopyr, it should have given you a complete kill.
Tilling is not recommended, because each little live piece that you cut up will begin to grow and it is spread this way.
Another possibility is to use the herbicide Tenacity with the active ingredient mesotrione.