we did this a while back using a mini-dv camera on a boom. With a monitor in his/her line of sight, the dentist knows to keep out of the way. Plus shouting “get your head outta the way” helps too!
Getting in close enough was the problem, but a telephoto adapter would have helped. Your widest shot will probably be chin to nose. A proper broadcast camera with a lens with 2x extender is ideal, but support becomes an issue. Little room for a jib in your typical dental room.
Deep in the back of the mouth, the lipstick cam idea might work, but you need light in there also, and the camera itself may block the overhead light. Maybe use a video laparoscope with a light source. Not sure you could rent that, but maybe the doctor could get a demo from one of the manufacturers.