I would consult a bc dentist it will cost you about 160.00 and wish you would have gone to bc dentist upfront as they could have done everything at once as they could have got those teeth out without the jaw being re-constructed I am sure. I think a dentist will be able to tell you better about this and worth the consult.
I would be afraid to also put under anesthesia again with those complications but did your vet use isoflurine or sevoflurine? It sounds possibly like they used sevoflurine which some vets are using now but it can cause hypothermia in dogs more so than isoflurine. Also ask what size tube they used was it cat tube or smaller?
Is your dog breathing ok now?
This is why i always recommend bc dentist for dentals as if there is a complication they are much more experienced to handle it as they go to further schooling for dentistry in dogs and the dentist does the procedure not a tech which in most dental offices it is a tech. Also most bc dentist now charge the same as vets do for dentals at least in our area they do and you being in new york it is pretty much the same cost here
This way if there is a complication with teeth then they do not have to go under twice it is all handled that day. My bc dentist calls me while dog is under and says here is the assessment and what i recommend and we decide right then and there what is done together like when demi lost 27 teeth he reshaped a back tooth for her as one root was bad but the other was fine so he was able to create a smaller tooth rather than pulling the whole tooth which is what a vet would have done.
I think the reason he did not want to pull those teeth is he did not want to break the jaw as if the disease is in the bone when pulling the teeth you can break the jaw. They have to divide the tooth and pull out one root at a time if a back tooth.
The jaw will atrophy usually when they pull the teeth especially in the front area where the front teeth are pulled. Where are these rotting teeth at?