Oh how sad, it looks like they no longer have the excursion we did with lunch. I went to the Disney site to find it and couldn't find it. The one we did was Green Grotto Caves with Lunch (FA47) we first went to the cave, which is huge!
Claustrophobia: They used to do concerts in it, which drove out the bats and the mosquitoes took over, so they stopped the concerts so bats would come back and take care of the mosquitoes. The cavern areas are really large, not claustrophobic at all. There was one small passage my daughter decided to try - it's tight, I went around the more open path and met her on the other side.
Bats: We like bats, but I know some people are not fans. They really weren't around through the vast majority of the cave. We did go into one cavern/lake area that was a bit crowded with everyone trying to see where we could see the bats sleeping above across the lake. Once this cleared out of everyone trying to see at once, it's not really a small area. It just seemed crowded due to the number of people wanting to see at once.
Mobility: There were a fair amount of stairs around a section, if I recall correctly it was to get to the area where you could see the bats. I can't recall now, if they had some type of transport for handicapped. But I'm not in great shape and was able to do it all fairly easily.
Lunch: This was really lovely. An amazingly breathtaking beach and a yummy meal. The best jerk chicken I've ever had. We weren't there too long, just enough for everyone to eat, and play a bit in the water/beach.
All total I think it was around 4 hours and we all really enjoyed it. I hope this helps!