Along with Symphony Swings, they also ask guests to leave bags on the ground for Soarin' (if it doesn't fit in the pouch under the seat) and Jumpin' Jellyfish. For all other rides, I've done as others have said, I've put the bag on the floor and put one leg through a loop to secure it. I've also seen guests wear their backpack in the front for rides that don't have chest safety harnesses (e.g., Matterhorn, Big Thunder, etc.). For Incredicoaster, I would look into a locker to avoid "being that guy". For the water rides, I've carried a small plastic bag with me to cover my bag (mostly to protect the electronics - like cameras, batteries, and phones - I've also just stuck those things in a ziploc inside my bag and let the bag get wet).
(Alternatively, depending on the age/height of your child, you can also leave the bags with the adult that is not riding. We've done that in the past when we had rider swap - the first group would leave their bags with the one that wasn't riding and then switch when it was the second group's turn.)