I think I may be able to contribute a little bit from my own experience. I grew up in a rural area in Sweden (not US as in the question, but a country with high, modern standard of education) in the 1980's, in a village of roughly 600 people (about 300 in the main village, the rest scattered in smaller villages and isolated farms). I also know about others who have been schooled in similar sized villages, and know teachers who have worked in such schools.
The main thing my answer will say that differs from the the question and the other answers, that I think can be helpful to make a realistic story, is that there will not be as clear cut job descriptions as in the question. With so few people, your job description will be based on how you can be useful rather than an organization chart. (There won't be any "the janitor", there will be a "<PERSON>".)
Our school was only grade 1-6, grades 7-9 was bussed around 1h away, the higher 3 to the nearest larger town also around 1h away.
All staff on these kinds of schools do multiple roles. Actually, all people in these kinds of villages do multiple roles.
For the grades 1-6, any adult with kid-handling-skills can teach all subjects except four: Sports and health, music, arts, shop. So, they had one class each but helped each other out on the subjects that required some special skills.
The school was divided in three classes:
1-2, the main teacher of which also took care of all education in sewing/knitting/etc shop-classes, and was the administrator and secretary of the school.
3-4, the main teacher of which also took care of sports for the 1-2, and taught all shop classes aimed at cooking/cleaning/etc. She also had arts, and was the librarian. The cooking etc. classes was not taught in the school but in her own kitchen. (Her property shared a border with the schoolyard. I think the unclear distinction between the school playground and her pretty garden, and the teaching involving knives and hot objects inside her home, might have made some insurance companies balk...)
She also had the after-school-activities for the kids who had to wait a bit longer for their parents to be able to pick them up, but that was not administered by the school - it was administered by the church.
5-6, the main teacher of which also was the headmaster, and took care of all music education.
Then there was a stereotypical manly-man, who taught sports, metal and wood-related shop, and was responsible for upkeep of the facilities. He was also one half of the two-man-team taking care of the gardening and the snow-plowing for the school and the church. 412
(The school and the church were closely intertwined.)
Finally, there were two ladies doing the catering and the cleaning.
There was a nurse, but she was only present some hour per day. Rather than school nurse, she was the nurse for the whole village, driving around over the whole district checking up on elderly people - but with her office in the school building. (Which meant that even if she had only very limited office hours dedicated to the school children, she was passing by and could deal with emergencies several times per day.)
Other friend have gone to schools with setups of 1-3, 4-5, 6-7, 8-9. 1-3 works fine, but higher grades than that can only be two at the times.
For grades 7-up you will need to have specialized teachers. They can realistically manage two specializations each. But they can all manage the lower grades.
The kids will need to be kept busy the whole school day, any gaps will lead to delinquent behaviours really quickly. But the younger kids have shorter days, and no kids have as long days as the adults.
So if you have one teacher per two years, you can cover the needed specializations, and still some. Three of them will have to be main teachers for the younger, but there will still be room for them to teach the olders - a bit of headache for the headmaster to piece the schedule together but fully possible. (Do not forget that also the headmaster can take quite many classes, even be one of the specializations.)
The support staff can take on some classes, but also be shared with church or home for elderly people. For example, cooking can be made both for the school, for any institution for elderly people, etc. that might exists.
So, i believe you will need:
* 6 teachers (if you really have all 12 grades), each with their different skills and interests. One of them double as headmaster, one of them double as administrator. They all do other small roles based on personality, skills and interests. 164