I don't see it as a university at all. I'm thinking grammar school.
By the time a student reaches highschool level work, they're either independent learners, or they're taking basic classes at the community college.
The point of a "liberty school" is not to indoctrinate, it's to instruct in basics. Math, reading, writing, and logical reasoning.
Government taught not as an ideal, but as a practical matter. That one change from what govt-run schools teach is part of logic. It's one thing to teach "here is the Constitution, isn't it great? That's why we pay taxes." It's entirely another matter to point out how reality differs from fantasy, be it in govt, religion, or history.
I was talking to my daughter today about this "liberty school". I would design it around the one-room-schoolhouse idea, with computers added.
Each student gets a subscription to Time4Learning.com, with a parent-student-instructor agreed upon daily requirement like "two lessons a day" (which is very easy to do), and when the student does a test the instructor will help the student understand any question they didn't get right.
Then there are group lessons, such as "addition & subtraction", "multiplication and subtraction", "fractions", "algebra", etc. The students who are at that level attend, regardless of age. Students who already know it help teach those learning. Questions are encouraged.
Someone takes a trip to NYC, they bring back pictures and present the trip to anyone interested. This teaches public speaking, with a question/answer period after the presentation.
The ham radio operator from the next town over comes by and presents what he does and how, with a question/answer period after the presentation. Dave Ridley can drop by and talk about his work. Etc, etc, etc.
I love reading Shakespeare plays out-loud, but there's no reason not to act it out if folks want to.
When I was in 4th and 5th grade, I was in an "open" school. It didn't work at all for me because they were so hung up on the fact I didn't make a "schedule" for myself every morning that nothing else happened _at_all_. But what struck me is that, with a little bit of motivation (like two or three or four Time4Learning.com lessons each day) to bring up subjects of inquiry, the rest of the day could easily be spent looking up interesting things that had been mentioned in those lessons.
"Shackelton did WHAT? Really? WOW!" etc.