Galloping does feel weird. Like others have said, it's ironically much less motion that trotting or cantering. Galloping to me feels like his back is not moving, but instead I feel two beats, hind end/front end. Just work your way up to it. If you need something additional to hold onto, try a neck strap. Just use a spare stirrup leather. It'll give you a little more security and also let you keep your hands steady and following his mouth. Stay in a light slightly forward seat, but stay close to your tack to so you can sit deep and back whenever you start to lose your nerve to bring him back to a slower canter.