My philosophy on closing the practice to new patients is not to. However, you can delay when they enter your practice (i.e. Dr B does not have a new patient appointment until December). If someone really wants to see you they will. Otherwise they will seek care elsewhere. When I did this I essentially stopped getting new patients for a few months. However, I had no choice since I was getting overwhelmed and could not service what I had (and subsequently lost some patients). Now I have a certain number of new slots each month to replace what I may lose (either through death, move, or dissatisfaction).
I would recommend trying to reduce your percentage of patients on MaineCare. I was like Martin and took Medicaid (called AHCCCS in Arizona) for the first several years (5) of my practice life. However, dropping those plans (there are 5 in my region) reduced the stress on my staff and the administrative burden, and I did not notice much of a drop in my income except for the first 1-2 months. It is a sad commentary that treating the indigent has to be such a hassle yet bureacracy has a way of doing that.
With regards to feeling indebted to patients, a good physician friend of mine once observed about a third of your patients love you, a third hate you, and a third are indifferent to you, and you'll never know who's who (though you think you may). (My friend by the way has one of the best bedside manners you'll ever see in a physician). So while many of us entered medicine to help humanity, the cold hard facts of practice life are you have to make business decisions on what is in the best interests of your practice and the type of lifestyle you want.
I hope this helps. Best of luck.