I think it is called the Great Goofini, is pretty mild. The ride lasts about a minute.
The next up, for now, is Big Thunder Mountain. It's really more rocking back and forth with a couple of hills. My kids love this thing. (So do I.) We usually ride it at least a couple of times. Riding at night is a different experience. They use fluorescent paint to change the mood. It was a few rides before I noticed the dancing at night in one of the outside buildings. The ride maxes out around 35 mph.
Next up is Space Mountain which is about the same speed as BTMRR. The big difference between BTMRR and SM is that SM is dark. You cannot see the turns as they come up making it jerkier. There are bright lights in some places but they are bright enough to make it impossible to see what is coming.
It sounds as if Rockin' Roller Coaster and Expedition Everest may be out of your desired range. Neither are like the coasters at Six Flags or Cedar Point.
The Seven Dwarfs Mine Train is in testing. I did not see a date for your trip. It might be open when you go. This is supposed to fit between Goofy and Thunder.