I would not talk to the owners. Might invest in a XL live trap and get the dog that way if shooting is not an option. It is pretty darn hard to catch a dog when it does not want to be caught. I recall the neighbors laughing as they watched me chase our new mini pin pup all over our then unfenced yard. I was frantic and very frustrated.
If I caught the neighbors dog I would SSS it or take it to a non-local pound. If they were making an effort to catch it, AND have a secure run for the dog to come home too then I might return the dog. If I have to spend my money,time,and chicken lives to get those dogs...then good bye doggies!