Among the wild birds the main rysk for AI introduction are migratory birds such as ducks and goose. These birds like open spaces where to fly, so the presence of trees around the barn could prevent their arrival and stop. In addition the removal of any source of feed and water in the parks could limit their presence.
In my opinion also the use of winter garden could be a possible solution to let the free range birds go out from the barn and at the same time avoid their presence in the parks.
About falcons…they could be an option to avoid the presence of ducks and goose, but they also could be one of the possible source of the virus.