If you're only here for a month I wouldn't bother. The only people who care are at the immigration office and you won't be going there. Airport immigration don't care one little bit
Not quite sure what you're having trouble with. The TM6 form was suspended a couple of years ago, now it's coming back as an electronic form. This is for ALL arrivals. The ETA is for people arriving without a visa and will be tied to the 300 Baht tourism tax. Is it that difficult? Is it the Thais who don't know what's going on, or is it foreigners who can't understand plain processes?
Just enter on a 60-day free entry stamp, if necessary get the 30-day extension at the immigration office. I think most dental procedures can be carried out in a three-month window.
Got one for my lady last year, it was about 5000 baht, although she paid a little extra (a few hundred baht) to VFS for additional service, which I think gave her priority service when she went in to do her biometrics