Since you have already ruled out any lameness, thank you for doing that ahead of this post, I would say its because he isn't paying attention.
If he's going around like a giraffe (you're not alone) he's not paying attention to anything but everything else around him. This means he's not thinking about where he is placing his feet, or really even picking them up. Time to start asking more from behind. He most likely is traveling on his forehand, creating more weight in the front, which then causes more tripping.
Why don't you ask for him to use his hind end/back? Letting him go around like a lama really isn't benefiting anyone at all, not you or him.
I personally would start asking him to work, sounds like its just a free ride for fun, which is fine, but its clearly dangerous or could be dangerous with one bad trip. Doesn't necessarily mean he needs to be forced into frame, it means he needs to be put to work, given tasks, and needs to concentrate. He can still go around with his head more out and down, instead the lama look. Work on leg yielding, and serpentine's, figure eights. Get the brain going!