Was browsing the blender subreddit, and came across this post about how to use the hair system. Before I had been doing it wrong! I prefer a cartoony system reminiscent of Neopets, and the trick is not many hairs to make things look fluffy, but actually almost no hair, and you manually add 5 or 6 strands. That way you have granular control over what's going on. Then you use a buttload of interpolated children hairs to fill them out.
https://www.youtube.com/watch?v=uETmTpskGU4 (its not a to-the-point tutorial, but the host has enough charisma to make wasting your time very much worth it if you vibe with his sense of humor.)