I think you misread this because he certainly did not say or imply "I was working on problems close to the gods", in fact the phrase he used was "when I seemed

I think you misread this because he certainly did not say or imply "I was working on problems close to the gods", in fact the phrase he used was "when I seemed to you to be concerned with problems close to the gods", meaning that others considered the things he worked on as being "close to the gods" only because they did not understand them at the same level he did - his list of experiments/problems was about how mundane the problems he was solving actually were. It did not read as him having much of an ego. Most of the problems he worked on have little to no impact on society or people's daily lives, most people still have never even heard of Feynman, and he knew most people wouldn't. That's not ego. If Feynman did have any ego it came from the pleasure he got from living an interesting life, not by how smart he was compared to the rest of humanity.