Here's another +1 on Mission: Space claustrophobia. I have only really experienced claustrophobia once in my lifetime (in an MRI machine), but probably the 2nd closest time was with Mission: Space.
You're guided into a "command module" that consists of a somewhat inclined chair/couch in a vertical clamshell orientation, and as you look across from you, you see a colorful control panel. Just before the ride starts, the module clamshell closes and the control panel is now literally inches from your face. You have enough room to maneuver your arms and press buttons and you can see other "crew members," but the sight of that control panel coming so close was very unsettling.
It was offset by the video of the "mission" starting fairly quickly after the module closed, which allowed you to listen for things to do that fairly readily distracted you from the very tight surroundings. On balance, it was a fun ride (I opted for the milder version), and I'll probably do it again this summer, but for someone with more substantive claustrophobia, I can't imagine it being something I'd recommend.