When I was a girl I rode bareback and did lean back at the canter--for some reason it is easier to keep in balance with the horse. Did sit up straight at the walk--rarely trotted:)
A comment about the horse with the gaping mouth--some horses just do that, especially if they are hyper. I have a little anxious-type mare and she will work her mouth and gape just standing around doing nothing. Don't use a bit with her and she gapes at the faster paces and when she wants to go faster than I do which is most of the time:)