Lawn Restoration

I bought a house last spring in the Baton Rouge area, and at first, the St. Augustine in the backyard was in great condition. Over the past year it had declined due to several factors, having two labs in the backyard (indoor/outdoor dogs, so not all the time) coupled with a wet winter, and we constructed a large patio off the back side of the house. During the construction process we inadvertently damaged much of the grass surrounding the patio area. This may have been mistake #1, but I seeded the area in early spring with Centipede as I did not want to sod the area. By May, it seemed like everything was looking good and the damaged area had returned back to health, though now I had a mixture of St. Aug and Centipede in the yard.

Fast forward to July, I notice buttonweed beginning to take in a few spots. I was not fully aware the damage that the buttonweed could cause and how quickly it would spread. I did some research and treated with MSM, but this was until about three weeks ago and it had continued to spread. I certainly noticed much of the areas that were sprayed had begun to turn brown and start to die, but there were still other areas where it seemed to still be popping up. Rather than chase it around the yard for the remainder of the year, I went off the deep end this weekend and began removing all the areas that I could identify by raking them up down to the dirt and removing as much root as possible.

What I am left with now is a large area (much larger than when we killed the grass around the patio) that has been taken down to bare dirt and several other patches across the yard that are also bare. I am looking for advice on what my best path forward is here to have my lawn back in good shape for next spring? I am open to all options, even if it means completely re-sodding a large area. The only consideration is that we have two labs that will use the backyard, but I am not opposed to temporarily fencing off an area to allow the new grass to take.

What is my best option here?