Your intuition is not objective.

You are being misled by a **bad plot**. Your data actually looks more like this:

<IMG src="https://i.sstatic.net/NIbbk.png" width="150" height="900">
<IMG src="https://i.sstatic.net/g4uZq.jpg" width="150" height="900">

Are you still convinced your "intuitive" solution is better? Split your data with a threshold on the x axis, and compute the cost function.

Just kidding. Normalize your data and this toy example will work.

If you intend to incorporate user feedback, **metric learning** may be worth looking into. If you learn a linear transformation, you can run k-means on the scaled data. Have a user select instances from the same and from different clusters to learn the projection.