Bless you Mokey! I have a lawn dilemma also. If the lawn is as bad off as 50 percent weeds and ick- crabgrass....overseeding may not give you what you are looking for. I have learned over the years that you really do reap what you sow. Having moved to Alabama a year ago and having time to evaluate our lawn- it is 50 percent crabgrass, 25 percent onions, and 25 percent mix of other weeds and grass. Needless to say- I will be starting it over from dirt once I clear it.
After studying sevreal guides about zones and observing the temperatures I was advised that turf Fescue seed is a warm weather grass that does exceedingly well here. In the fall when it begins to die down you can overseed with a Zoysiagrass- cool weather grass- to keep a green lawn year round. Zenith/Compadre are both good Zoysias. And Combat Extreme or Scott's Fescue are good. Best of luck to you!