Dear J.,
I do think that your son is very likely to come back home, otherwise, he would not be in communication with you. To me this means that he still loves you and that it doesn't all have to do with you or your relationship with him. There may be other factors that are motivating him to stay away such as wanting to seek adventure, being his own person, an involvement with drugs or other issue. He may not be running AWAY from you, perhaps he is running TOWARDS something, even if that something is against the values that you tried to instill in him.
I don't think that you can even get the police to bring him back forcefully unless he is a danger to himself or others. As I remember, you did talk with the police but they were not too eager to help bring him back. You may want to inform yourself of the options regarding legal action, as he IS a minor and you as his legal guardian have certain obligations. But I am not sure what you can really do besides drag him home forcefully. If you decide that this option is necessary (to protect him, yourself, and/or the public), you will need a clear and decisive plan to keep him home. Not easy as a single mother of a 16 year old. But if you do bring him home you need to have a firm support system and a workable plan. Otherwise, all he will do is leave again.
Again, I do think that he will come home eventually. The issue is whether you are willing to wait patiently for him to do it on his own or not. It is important that you have a plan for his return. I think that leaving this plan up to him is not a good idea. Asking him constantly what he wants may increase his sense of not being connected to you. Perhaps changing tactics and talking about what you have honestly learned from this experience and what you would do differently might give him a better sense of what he will find when he does return home.
As you do more homework to find resources for yourself and for him for runaway minors, you may want to share that information with him. As saying, "Hey son, I found out about this program that provides health care for teens. I talked with so-and-so and she seems really nice. If you ever need any health care, she can help you. Her number is ***. Thought that you would like to go there. Take care, Mom." You can also find resources to help yourself and share this with him. So you can say "Son, I started going to this great group therapy sessions for Moms with runaway teens. It is located on **. I go on these dates**" It is really helping me. Thought I'd let you know."" I am not sure what you may have available in your area, but I am sure there must be something as you are not the first mom going through this.
Hope that this is helpful and that you find the help you need. Hang in there.