Neuroanesthesia is, IMHO, like trauma and OB. I don't think anyone needs to do a fellowship, unless perhaps you want a career in research. (and even than, you probably don't need to do an extra year) You're a resident. Tell the scheduler you want to do as many neuro cases as possible, and continue to hound them. (yes, I'm sure there is a "neuro resident" on a neuro block, but he/she can't work every day, or do all the cases. You can become the go-to guy when they have an opening. Find out if a neuro anesthesia attending or surgeon is doing any research and try to get involved.
Find a job, academic?, that does a lot of neuro. Maybe a place with a neuro fellowship.
😉 Ask to join the neuro team and seek out all the guys there with grey hair. Academic attendings don't mind getting the junior faculty up to speed. It's not like it's neurosurgery.

Instead of losing ~200k on another training year, go get a job in academia. If you don't like it, find a PP job and quit after a couple years. You'll be a better applicant as well.