Hi Johnna! Super question! I love how detailed you are with your planning!
While there may be a handful of others, I can tell you from personal experience,
Astro Orbiter at Magic Kingdom and
Soarin' Around the World at Epcot are two attractions where bags are not necessarily with you at all times. On Astro Orbiter, our bags were placed on the platform next to our spaceship. During Soarin' Around the World, larger bags are placed on the floor in designated areas while smaller items can be stowed under the seats.
Kali River Rapids at Disney's Animal Kingdom Theme Park provides complimentary lockers where your items may be stowed temporarily while you enjoy the attraction. You are not required to use a locker but I highly recommend it as you and your items will, most likely, get soaked.
If needed and depending on the age and number of Guests in your traveling party, I recommend splitting up your items into smaller bags. There have been many times I have stuffed my backpack way too full of "needed" items. Bulky bags can become a bit of challenge in small spaces on some of the attractions.
I hope this helps you with your planning. Thanks so much for sharing your question with the Disney Parks Moms Panel! Please let me know if you have any other questions as you plan your magical Walt Disney World Resort vacation!
Kari