I fiddled with it some more, tweaked the colors towards Magenta instead of Red and added another layer:

- I copied the sharpened original layer again and desaturated it. Then I changed the Levels, so most of it would be white, and some of it would be black, like this:




I set this to Soft Light: (in other tools the closest is Overlay at very very low opacity)

Result:


It's more contrasty around the edges now, and lighter overall. A bit closer to the goal.