Note that whether electrons are spherical or not is important to theoretical physics. Right now we do NOT want them to be perfect spheres. But, as you say, our

Note that whether electrons are spherical or not is important to theoretical physics. Right now we do NOT want them to be perfect spheres. But, as you say, our ability to measure this is limited by our instruments. Keep in mind that many important scientific theories had to wait a very long time until our instruments could reliably measure what was predicted. For example, theories that the earth rotated around the sun were theorized as far back as the 5th Century BC and maybe far before that. Actually proving the Earth rotated around the sun didn't happen until 1728 by measuring aberration in starlight. But what the ancients actually sought, proof by stellar parallax, was far beyond the capabilities of optical instruments until 1854. To be technical, it was actually empirical to believe the sun orbited the earth during this time. Ancients would say "if the earth orbits, I should see stars shift. I do not see stars shifting, therefore the earth does not orbit." Aristotle actually used this very argument! I was listening to some of the researchers comment on this particular discovery and they are more hopeful about the technique than the findings. There is already talk about improving the resolution a couple of orders of magnitude.