How can I sharpen edges on a heightmap generated landscape?

I’ve used terrain.party to generate a heightmap png of a real location on earth. This place has a lot of sheer cliffs above gently rolling hills. The rolling hills are all good, but the plateaus above the cliffs kind of roll to a gentle bevel off down the cliff face, rather than being a sharp edge. The upper image would be a cross section of how it is now, the bottom one is how I’d like it to be: https://i.imgur.com/2F8Yg9n.png

I’d still like to preserve the gentle roll of the lowland hills, and some of the natural variations on the plateau on the cliff face, so I don’t want to do anything to harsh, I just kind of want to pinch out those bevels so they become more of a sharp edge than gentle bevel. Same goes for the foot of the cliffs.

How is this done?