You know dental care doesn't come cheap. I think Delta doesn't cover major work, partials, crowns, root canals, implant - till the policy has been in effect for 12 full months. If you bird is young enough it may cover braces etc. Try using those dental rinses for gum disease etc...
I'd forget about a rabies risk and think about the poor chicks welfare. Obviously she needs either an extraction or best case scenario, root canal and eventual crown.