First, talk to your new neighbors.
“Good evening, I’m RoosterRedux, and I wanted to have a word with you about Spot.”
Keep it polite, factual and civil. Document the conversation. If your state allows one-party consent for recording audio, you may choose to record the conversation to establish this was done.
You don’t have a dog problem, you have an owner problem. All dogs should be properly obedience trained and socialized—it sounds like this owner hasn’t been doing a great job so far.
Hopefully, if he is a believer, this will be the wake up call he needs to see a concrete way to show love to his neighbor.
That was my first thought also...but the humane society folks said that's NOT the best way to handle it. Could lead to unnecessary neighborhood tension if the dog is ultimately picked up by Animal Control.
The very fact that the dog is loose demonstrates that there is a problem. Humane Society folks even suggested waiting a few days to call animal control unless the dog is still running free. They said the dog owner doesn't need to know if or from whom a complaint was received.