DeeDee, I'm probably not your best "expert" to comment but I can understand your interest and enthusiasm. I'm also almost in the opposite corner of the country from Florida.
I have some experience seeding pastures but not necessarily for chickens. And, I've used a pasture mix for seeding a lawn. My interest in choosing a pasture mix for livestock was having a good percentage of white clover with the grass seed and I really wanted clover in the lawn, as well. It worked great! Now, I'm not saying it was a lovely suburban lawn - I lived out in the country. The hens foraged thru it and enjoyed the lawn a good deal.
I've read that one of the advantages of pasturing poultry is that weeds are eliminated. So, the chickens are eating the weeds as well as what has been planted for them. That seems fine to me.
I did some searching and came up with only a little on the 'net. A study at Truman State University was in 2 locations but the pasturage was only described as mostly grass in one location and high-legume alfalfa" in the other. Research at the University of Minnesota on pastured poultry had a bit more to say.
http://www.misa.umn.edu/vd/publications/PYW_CH5_Management_alternatives.pdf (fairly long to load):
"Pasture should be planted with a special forage mix. Remember that poultry are not ruminants and therefore wont do as well as some other livestock on predominantly grass pasture. Chickens, for example, are said to prefer broad-leafed plants and legumes, such as alfalfa and red clover, to grasses."
You could allow lawn grasses to grow enuf to mature seed but that would hardly be practical even if the hens would benefit and appreciate the seed. So, legumes should be a focus in any lawn that you plant for them and represent a good percentage of the seed mix. By the way, that interest the hens have in grass seed should be a caution to you. Also, consider their love of digging and dusting themselves. They could do a great amount of damage to the lawn if it is not allowed to first establish itself.
Now, I hope you have more Florida-specific ideas from other folks.
Steve