Howdy Florida Neighbor!
Don't do it.
Yes, expand the run. Good on you. Nothing but benefits for your birds.
Don't sod. They will destroy it.
Florida has few successful native grasses. In the area typical of something described as a "run", there is nothing which roots deep enough, grows fast enough, and is otherwise hardy enough, to survive chickens for long before exposing bare patches and all the rest.
The ONLY way to change that is to have a very small number of chickens in a very large space. Even then, they will make pits for dustbathing, they will make bare spots scratching, and seasonally, its going to go brown and get destroyed regardless.
Others have acheivd success by planting outside the run, where it is protected from the chickens, and letting it intrude into their area as the plant expands. I've found this a good way to protect new plantings of mint, oregano, clovers, and grasses that expand via runners (i.e. St Augustine). My pasture also has success with clumping prarie grasses, because the clumps are resistent to destruction, and some prarie grasses are deeply rooting (bluestem is a good example), but that's not native.
Mostly, however, you are going to have to find a method that works for you, and satisfies your sense of aesthetics on your property. The soil I have here, with its deep water table and heavy clays is hugely different from the high water table, high salt, low nutrition grey/white sands my parents deal with, or with the shallow loams we had in pine barrens when the family lived farther inland - which was still better than the sugar sand of the Ocala area.
Don't do it.
Yes, expand the run. Good on you. Nothing but benefits for your birds.
Don't sod. They will destroy it.
Florida has few successful native grasses. In the area typical of something described as a "run", there is nothing which roots deep enough, grows fast enough, and is otherwise hardy enough, to survive chickens for long before exposing bare patches and all the rest.
The ONLY way to change that is to have a very small number of chickens in a very large space. Even then, they will make pits for dustbathing, they will make bare spots scratching, and seasonally, its going to go brown and get destroyed regardless.
Others have acheivd success by planting outside the run, where it is protected from the chickens, and letting it intrude into their area as the plant expands. I've found this a good way to protect new plantings of mint, oregano, clovers, and grasses that expand via runners (i.e. St Augustine). My pasture also has success with clumping prarie grasses, because the clumps are resistent to destruction, and some prarie grasses are deeply rooting (bluestem is a good example), but that's not native.
Mostly, however, you are going to have to find a method that works for you, and satisfies your sense of aesthetics on your property. The soil I have here, with its deep water table and heavy clays is hugely different from the high water table, high salt, low nutrition grey/white sands my parents deal with, or with the shallow loams we had in pine barrens when the family lived farther inland - which was still better than the sugar sand of the Ocala area.