My guess is the wrongness is either a lack of fat or overcrowding, or both. Fat (butter, margarine, oil, whatever, I prefer butter) acts as a flux to spread the heat. Use enough, plus use proper tools.
"Butter seemed a little risky at that temperature, so I went with olive oil, in a cheap, lightweight nonstick skillet. In five minutes, a few flecks of brown had appeared". Olive oil is good for many things, but not for frying things. The "few flecks of brown" sounds like there's not enough of it either, so the heat oil gets applied where the onions touch the skillet directly. Add more flux until the flux generators cannae take it any more, Cap'n!
Just to prove my point, here's a timelapse of half an onion done in butter, the way I usually do it. Quality skillet, induction stove set to my favorite level, 7 of 9. 5 minutes and they're good: https://photos.app.goo.gl/tpfAy5uqc6NRRFsB8
If you want to be more careful, you can lower the heat - here's me cooking the other half onion at 2.5 out of 9, which is really very low (though done on a warm skillet, so it's a bit warmer): https://photos.app.goo.gl/QLaW7YkqijxF7K95A