Just an update for everyone wondering how things went.

The extractions went as planned. Some of them were a struggle, and the dentist needed to apply a lot of coercion to get some of the deeper roots to finally pop free. He needed all two and a half hours to get it all done.
They needed to grind down some bone around the infection site, and suture it closed, but it should heal well, after some days/weeks of discomfort.
I was accidentally overcharged initially, but will be getting some of that back. Nevertheless, I will need to be very creative with my bills in order to get everything payed. Still, the dentist is fully paid, so that's one BIG bill I don't have to worry about. I'm also watching rent, so it should only be smaller bills like insurance and Internet that will suffer.

Thank you to everyone both here and in real life that has been supportive and encouraging while I go through this. It's been a whole week of hardcore adulting and more than a little discomfort, but the hard part should be over now.