If I ride an animal, like a horse, when I leave the Border it feels like I'm going to be backtracked. But if I ride a Happy Ghast, I don't get backtracked. I feel like I can keep going, it might be a bit twitchy. I'll come back when I Shift-out of the Happy Ghast.

Are you saying it doesn't work like any other mounted entity or vehicle? Can you share a video of what you see when you try it?