There is an excellent dentist -Dr. Unno- I've used many times in Matsuoka (Fuji), diagonally across the intersection from the Potato supermarket (towards the ocean from Jumbo Encho, towards Shizuoka from Fuji Central Library/International Lounge). He and his staff don't speak any thing but Japanese, but are very good communicators nonetheless.
Not being on Japanese national health insurance was not a problem; in fact, the prices were very reasonable. I got a receipt and submitted it to my insurance provider (or not, depending on the price/situation).
Here is a map/picture of the location-