Hiya Tammy!
Welcome to planDisney! I love how you are planning and checking the
My Disney Experience Mobile App to see what Lightning Lane times are available! I am typing this answer on a Sunday at approximately 4 pm and I see what you stated in your question. Both
Remy's Ratatouille Adventure and
Frozen Ever After show "LL Disney Genie+ Not Currently Offered." These
attractions are still eligible for Lightning Lane but they are usually the two attractions that run out of time slots first in EPCOT. If you check out the Tip Board at 7 am I am sure you will find that there will be Lightning Lanes available. Most likely by mid-morning on busy days the Lightning Lanes will run out. There are only a certain number of Lightning Lanes available each day for an attraction. As a result, these are the attractions you should prioritize each day when trying to book a Lightning Lane. Pick them first or you will miss out.
Starlight Safari at Disney's Animal Kingdom Lodge sounds pretty exciting and as I never had a chance to experience it I reached out to my planDisney friends. The always helpful
Elaine let me know that she enjoyed her experience with Starlight Safari and saw giraffes and zebras. She loved looking through the night vision device which fulfilled her dreams of being on a nighttime pirating adventure. However, she felt that the animals could be viewed just as well from
Disney's Animal Kingdom Lodge lobby at the Savanna Overlooks. She did state that the best part of the tour was the Cast Members who were so informative and kept her captivated. I'm not surprised as it's the Cast Members who bring the magic to the Parks.
I hope this helps and you have a great trip!
Happy Planning!
-Nimmy