Have you ever tried baking them in the oven on cast iron?
We have a cast iron cookie sheet, when everyone wanted eggs in the morning it was easier to crack a tray full and bake them. Takes above 8 minutes at 350 , but ovens vary.
They turn out with whites almost like they were poached, but over cooking can make them a bit too firm.
Edit: My wife was preparing two of the last three egges, leaving just one egge for me. Since I wanted two egges, that was insufficient, and so I prepared zero egges.
Knowing that one egg would joy be enough, that would have meant also making a little bit of something else. I did not want to prepare two different things.
Instead, I just made a sufficient amount of something else.
What skillet are you using there? The texture makes me say it's something modern. Lodge is a huge brand right now, so that's my guess. And the eggs size compared to the diameter make me say 8". Am I close?