Safari is quite bumpy, too.
I had to avoid jostly rides our last trip there (though it wasn't my neck, so you may be a little different). Honestly, we did a LOT of walking around to take in the atmosphere and people-watching. We watched a LOT of shows (Tiki Room, Carousel of Progress, American Adventure, Tough to be a Bug, movies, etc.), too.
The rides DH and I deemed safest for me were the TTA, Buzz Lightyear, Peter Pan, Winnie the Pooh (though the cars do bounce, but not terribly hard), Little Mermaid, Haunted Mansion, Pirates, Small World, Soarin', Gran Fiesta Tour, the train to Rafiki's Planet Watch/Conservation Station, Great Movie Ride and Toy Story Midway Mania (though I might avoid that with a neck problem - it's jerky when you whip around to new games).