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one-day-a-week public school I'm enrolling her in. (Essentially, a school for homeschoolers. It provides a community, some fun learning, the official mantle of school enrollment...
Are there other options such as a home school co-op or a private school with a "University model"?

There may be a downside to this public school since "the official mantle" of government schools may include tracking progress, collecting/sharing student data, mandating testing, and overseeing or dictating to parents. You may wish to keep well informed of this school's policy and practice, including any changes.