Wow! He is really a lovely horse. Maybe you could just try it a few yards at a time and keep it to a slightly slower pace and then increase gradually. Say, I am going to hit the gas to the half way across the arena, then all the way to the end etc... He sure looks like fun.
I agree on the use of the helmut. They also have the spine protectors which might make you feel extra snug. He seems to be a well trained, willing horse. Hope you guys can gain confidence together.