Horseshoe theory seems to me like declaring North on a compass rose to be "middle", and saying as you go further "east" or "west" around the compass, the extreme east and extreme west gradually become more similar to each other.

Which is in fact true. Perhaps a more apt analogy is that, as you go north, east and west become less distinguished, up to the North Pole, where going east and going west reduce to spinning around yourself counterclockwise or clockwise while standing at the same spot.

In this analogy, the North Pole would be ideal totalitarianism, where the government micromanages its subjects' lives in great detail, it is always right and doesn't even have to explain itself since it is its own source of legitimacy, and nobody can question its ways.
Real-life North Korea sits close to the North Pole.

Classical liberalism/"Progressivism" would be perhaps the South Pole or maybe the Equator.