I have neck and back problems, without going into details, it is Arthritis with a very bad atitude. I can do test track, but if you look at the picture they take, I am in a full fledge grunt to minimize the shock to the back. I do the same with most of the other rides, that I will go on. Here is the list that I find that I don't have too much of a pain issue.
Rockin Roller Coaster - I found that I can hold my grunt for over 60 seconds!
Test Track - The road simulations are the worst part.
Mission Space - No jerky movements, wonderful experience. However with the heart condition, I would make sure he is ready for it.
Tomorrowland People Mover - Oh, wait, it doesn't hardly move. I highly recommend this to ride over and over if you have a kid that needs a nap.
Tower of Terror - I didn't like the unpredictability of the elevators, my wife and mother in law rode it once to check it out, they said, no problem. I got on, and it happened to be one of the sequences that had a slight jerk, that hurt.
I won't ride any of the motion simulation rides like star tours, those just make me writhe in pain, Not worth it.
One fun one that we found was at DisneyQuest, where you build your own coaster then ride it. the ride was ultra smooth, and we had a fairly aggressive coaster built.
As the cast member recommended, "Be on the safe side". My wife sees my pains and listens to me whine about them. She is a pretty good judge of what I can handle. I would urge you to do the same.
Best of Luck!