Also, you could try Dr. Christopher's Herbal Tooth and Gum powder. It contains white oak powder which is supposed to be excellent for regrowing the gums. He advised putting the powder in the entire tooth area between the teeth and gums every night for 6 days at a time always taking the 7th day off.
The topical calcium products at calcium therapy.com would probably be helpful. The owner of the site, Dr. Manhart, is opposed to the deep cleaning. He may be able to give you some advice (he is very accessible and helpful via email).