I am extremely claustrophobic and am able to handle the stretching room as long as there isn't a huge crowd. If the standby line is long, I know the stretching room will be packed. I use my GAC during these times and a CM still takes us through a stretching room, but - with a much smaller group of people (only the guests entering through the wheelchair entrance). Unfortunately, the stretching room still opens out to the massive crowd waiting to squeeze down to a single line to board the ride. The only way to avoid the crowds is to ask the CM to allow you to board through the exit and skip the stretching room all together.
You didn't ask, but, I'm gonna warn you anyway about the Soarin' ride line at Epcot. It's a HUGE massive crowd that is about 10 people or so wide that eventually will funnel to a single person line. You may want to avoid this altogether depending on how bad your claustrophobia is. Fastpass or GAC is the ONLY way I can handle waiting for Soarin'.
Another problem area for me is the snake/waiting line for the Great Movie Ride at MGM. It's one of those lines where one can get stuck in the middle of a crowd with no visable escape.