But that was because humans were watching you. I imagine it would be notably less stressful if you were being watched by an increasingly large population of chimpanzees instead of people.
Personally I imagine that the larger that group of chimpanzees got, the more relaxed I would feel. Just think about solving a problem in a room with 1,000 chimpanzees just chilling out and watching without a single other human in the room.
Likewise I suspect chimpanzees would perform different if watched other chimpanzees.
Obviously a chimpanze recognizes humans as something like itself, and that the humans opinions matter. At the very least a chimp knows that the humans totally control it's life.
You have a very different understanding of the relationship between yourself and any group of chimps.
But when I was a beginner at it, the stress was indeed crippling.
The cure for that kind of stress is to keep doing it, the stress will go away. Like if your throat freezes up when stepping behind the podium, just take every opportunity you can to public speak.