I think you are likely right that this is about meeting her social needs. If your instinct is that unschooling will serve her best educationally, a number of possibilities for meeting social needs spring to mind.
1. Reach out to the local homeschooling community, regardless of the predominant religious motivations for their homeschooling.
2. Take a more active role in securing social opportunities in the after-school hours. Extra-curriculars, play-dates, sports, etc.
3. Look for social opportunities that aren't necessarily with other children, but are available during the day. Nursing home visits, volunteerism, etc.
4. Consider driving to a larger town to connect with a different homeschooling crowd.
5. Could she go to the public school for lunch, to socialize? Our local school happily allows this.
6. Part-time enrolment in the Waldorf school. If it's a new school, they might be open to this. You could negotiate a fee much less than regular tuition, and maybe have her attend a day a week -- maybe whatever day has the most art / theatre / outdoor education. It would involve some driving, obviously, but maybe it would be a good compromise.
(whose unschooled 8-year-old is attending the local public school this week for the Arts and Writers Festival)