Reality is weirder than fiction these days.
The more I learn about people the more I like cats...
Wild turkeys can fly quite well. I’m not sure how far, but they can and do fly.
If they want to do this, why not let them fly to begin with from a low altitude hot air balloon? About 100 feet would be quite possible and probably not harmful to the birds, quiet enough it wouldn’t stress them out a lot, and on release just let them fly away on their own. Trade off is it would take a bunch of balloons, but that would draw tourists too.