Hello Xisca,
That's good news with your precipitation, as it's just enough to grow the crops I mentioned in the previous post, and your summer temperatures are perfect to for those warm season crops.
My suggestion is put down a little lime to get your pH around 6.75 to slightly sweeten your soil and improve your grass growth. A little lime will also help growing legumes to, as lime also has calcium in it.
Another suggestions that may grow there in your cool season is Common Vetch, it's an annual climbing legume.
A Sudangrass-Sorghum Hybrid for grazing may produce more forage then Sudangrass alone, and may be more drought tolerant then Sorghum.
Common Vetch is a annual legume that will most likely grow in your cool season with the grasses fixing nitrogen, and may even grow a little in first part of your warm season, though im not sure how well it will reseed without chill hours.
Sainfoin is a perennial fodder legume worth at least looking into, but without proper chill hours in your frost free climate, I'm not sure how well it would grow there as a perennial.
Don’t forget to look at the Silver River Sweet Clover cultivar, as its drought tolerant and does well in heat compared to other sweet clovers, even in southern Texas. Which if I'm not mistaken in parts of southern Texas is very close zone 11.
Because many cool season legumes tend to be deep rooted, they may stay green a little longer then the grasses, helping transition your lambs with high protein forage while the the warm season crops get their growth established.
The Sunn Hemp, Sudangrass-Sorghum hybrid, Teft and Millet I already mentioned will all be your best options for fodder in the warm season drought, as they are proven in your climate zone. And if you were to only pick one Sunn Hemp is it, followed by Sudangrass-Sorghum hybrid as a close second, then Millet.
If you can do sprouted grains, look into a sprouted grain
fodder system. It increases the dry matter content exponentially, and the protien content, because you let the grain sprout to around 6 inches tall, making it comparable to quality grass forage. Using it as a supplement at minimum shouldn't be an issue, as many people do already with Barley.
I would look into a mix of Barley, Corn and Peas if possible, to create a more balanced nutrient content of fodder, then make sure they have access to other free choice supplements and quality grass hay.
The sprouting changes the enzymes of the grain itself, which also changes the seeds chemistry, and in many casses can reduce anti-nutritonal properties that are sometimes a problem in legume seeds.
Doing some research on a good sprouted fodder mix will help insure balanced nutrition, without causing bloat or nutrient deficiencies, especially from anti-nutritonal factors associated with legume seeds. It will also let you know what percentage of their diet you can fill with with the sprouted fodder.
Definitely research any sprouted fodder mix from accredited sources before implamenting.
Hope that helps give you some ideas!