Update (in case someone else comes across this post looking for help):
After asking around and consulting with vets, * Isoflurane gas * is the anesthetic recommended for hedgehogs needing anesthesia.
I went to a different exotic vet (farther away and much more expensive, but lots of hedgehog experience) and that is what they use for anesthesia on hedgehogs.
Pinecone had his dental work done there with no problems and by the evening he was very chipper and seemed to be feeling better already
Much different experience than with the other anesthetic that was tried! I'm just thankful nothing went seriously wrong!