It's wonderful that you've researched this so well. I have some extensive - and expensive - dental work coming up and I always dread the worry over gluten in his office. This has done a lot to reassure me.
Did your research also show dental floss to be gluten-free? A long time ago there was a discussion here about flavored and unflavored dental floss. It was surmised that Reach dental floss was safe in the unflavored varieties but not the mint or other flavors. I've stuck to the unflavored kind but still have about 4 packages of mint stuck away for my husband's use. Do you think they're safe?
Since then I've always taken my own floss to the dentist when I go in for cleanings but it would be nice not to have to worry about this.
I do not use flavored dental floss because I like the unwaxed variety and that does not come flavored. I used to use the mint type when they did make an unwaxed, flavored mint type but that was pre-diagnosis so that won't help you at all. I would stick with the unflavored, unless you want to call the company and go through that exercise of trying to verify it's status. It can be a total pain....I spent weeks calling everyone but got the information I needed and learned a lot about dental products. I have had extensive dental work done and will, according my dentist, until I am no longer on the planet!
To add to this....I go every 3 months for full cleanings, have had multiple caps done, I am in the midst of having 2 dental implants done.....you get the picture. I am sending my dentists kids through college! In all this work, I had one severe reaction and that was from the impression compound. It was the damn gums, which I verified later by eating some gluten-free baked goods I made using gums (I normally do not use them in baking). I felt crappy afterwards so do not eat them anymore. My dentist knows how careful he has to be with Celiacs....I trained him well. Go ahead and get your teeth fixed and, as long as you do the homework and make sure your dentist is on board with everything, you'll probably do fine. Teeth are important!