y'know ... I think my experience with handstand is comparable. I learned to balance rightways up as a child and don't remember much about the experience, which is why I didn't think I had anything to contribute to this thread, but learning to balance upside down is something I never could get as a child, and only learned a couple of years ago.
The first time I went into handstand my yoga teacher held my legs and I was so terrified I literally shrieked. It's still very slow progress getting my heels off the wall ... I think my PR is six seconds
... but before I hurt my shoulder I was plenty comfortable in headstand in the middle of the room, and I can go up into handstand at the wall pretty much effortlessly. It really was an ah-ha moment when I felt my body in balance. I think having the courage to try until they get that ah-ha is something they'll need to find within themselves, but it sounds like you're doing what you need to, to help them on their journey ...
Speed comes from what you put behind you. - Judi Ketteler