Kitty. Cannot see a solution to your problem with your cat's safety as well as its enjoyment of life. The coyotes probably will be around the CR466A area because of all the recent development in the Villages' Southland. If they trap one or two that still leaves the others that have been displaced by the recent house building.
Do you still have a big dog maybe it should keep watch on the lanai?
I do think most coyotes will high tail it whenever they encounter a dog bigger than they are unless the dog is very submissive. One of those motion sensors that sets off a dog barking?
REX Entrance Alerts with Barking Dog Sound