June, out our way, we call Animal Control. I know it doesn't sound like the most humane organization (dog catcher comes to mind) but they are. They rescue animals and, if necessary, will get them to an organization that will help them.
I live in a rural, small town, but I realize that it might be different out your way.
Regardless, if animal control can capture the poor thing, and they're willing to give it to you so that you can drive it to the rescue facility, that might be helpful. Let them do the difficult work, right?
I hope Droopy will be okay.
