"I am fairly certain they are being "cared" for. They seem to roam at predictable times, not just all day. "
That really sounds like they live near you. Have you met and checked with your local neighbors in a 360 deg. area around your place? I prefer to try to find the owners before I trap or shoot, sometimes they don't know. You will have to move fast on this as it sounds like they are getting braver. Pics or video of the dogs at your place will go a long way toward convincing an owner. One dog is a dangerous nuisance, two dogs or more is an emboldened pack.