Yes, there is absolutely a link between hyperthyroidism and dental health. In fact, there is such a strong link between thyroid problems and dental problems that dentists are taught to look for signs of thyroid impairment when they are doing regular dental exams -- they can sometimes be the front line of defense in an undiagnosed thyroid patient. And they sometimes must react with modifications to dental care -- for instance, the use of anesthesia -- when a thyroid patient is in an acute period.
Here's one article about this; scroll down to where the subhead says "Thyroid Oral Implications:"
I assume your dentist knows you are hyperthyroid? Have you talked to him specifically about your teeth and the changes you have seen in the last three years? Do you feel like he is knowledgeable enough in this area? If not, I wonder if your endocrinologist could refer you to a dentist who is well-versed in thyroid issues?
I am really sorry to hear that even your doctor fears that you could have a heart attack at any time. Have you two discussed the removal of the thyroid gland altogether, even though it would mean a lifetime of meds?