Back yard redo - Weeds out of control
I sodded my ~7500 SQF back yard with St. Augustine after my home was constructed in Houston TX several years ago. The lawn looked great the first year or so but began declining afterwards. The fact that the yard is large and doesn't have in ground sprinklers was likely a major factor as well as what looked like dead patches from disease or insects. I applied fertilizer and weed killer every year but the new growth of the grass couldn't keep up with the growth of the weeds in the bare patches. The lawn (or perhaps field of weeds is more accurate) is now almost if not entirely taken over by weeds. There are a few patches of grass near the fence to my front yard which was also St. Augustine when sodded but has since been taken over by Bermuda.
As you can see from the picture the yard is an eye sore to say the least. I have an assortment of various weeds and plan on trying a liquid selective weed killer to try to better gauge how much if any grass is left. I purchased a hose end sprayer and am ready to get the weed killer concentrate and could use some recommendations as to which is best. I'd like the strongest herbicide that won't affect any desirable grass that I may have back there but that also won't remain in the soil and prevent new growth since I plan on seeding with Bermuda in a few weeks. I know I don't want one that contains atrazine since that would interfere with new growth.
My other question is how to best handle the preparation of seeding of the new lawn. Since the yard is large I don't want to spend a fortune after having already spent so much sodding. I know it's recommended to loosen the soil to prepare it before seeding but this isn't realistic on my budget. I know winter grasses are often seeded here to have a green lawn during the winter months and those obviously are just over-seeded without any loosing of the soil. Since I plan to try to get up as much of the dead weeds and thatch by scalping the lawn and bagging it, would I then be okay just broadcast spreading the seed directly onto the unloosened clay soil? There are power lines directly behind my back fence that attract birds and I'm concerned with the seeds being eaten by them but covering 7,500 SQF of seed doesn't seem practical. Anyone have advice on the best way to handle this?