i recently put on Scott's winterizer.
Oh boy, I've been there. You've just set yourself up for some very healthy weeds.
If you are in DFW then you've missed your best window to plant new sod.
Let the soil dry out between waterings at least an inch down. In DFW, I have to run my system only once or twice from Oct through May. I dig my finger down and see if its moist during the dormant season and during the active season I also observe the color and folding action of the leaves. I'm looking to see if the leaves hold a tight vertical fold beyond the hottest part of the day.
Apply 10lbs/1000sqft of regular corn meal every 6-8 weeks through spring. Spot treat trouble spots by spraying milk.
At the end of March apply a 1/2" of organic top dressing compost to the lawn.
In the spring, let any competing Bermuda blend in but hand pull like crazy the crabgrass, Dallis grass and other weeds before they can drop seeds.
Mow as low as possible to encourage Bermuda and SA to spread to bare spots until full coverage, then mow as high as possible to encourage the SA to dominate again.
Get off the chemicals immediately, a half-committed approach will hurt you. Good luck!