No experience with this but after I'm quoting from a web site that tests for such disease and it says.
....for birds "treatments involve the use of tetracycline and its derivatives such as Vibramycin, Doxycycline, Oxytetracycline. The antibiotic can be given by intravenous or intramuscular injections. Antibiotics can also be given orally or mixed with palatable food. Treatment periods generally last about 45 days varying slightly depending on the treatment. *Calcium should be withheld because tetracycline binds to calcium. Citric acid in the bird's drinking water can increase the levels of antibiotics in the blood.
*In humans tetracycline and its derivatives are generally an effective treatment for Chlamydia."
Symptoms for humans if contracted from the birds and it is a zoonoligical disease are
"Transmission of the Chlamydial organism from birds to humans has been confirmed in a number of cases. Although psittacosis infection in humans is rare it is potentially dangerous for persons who are sick, elderly, immunosuppressed (e.g., HIV patients) or pregnant. These people should consult their doctor for more information concerning Chlamydia psittaci. "
I would look carefully at the possible transmission to humans before I decided not to cull and whether you or any of your visitors to your place could be at risk since this is an airborn disease.
Take care.