PNG to height for print

I'm trying to modify the height of a plane (or a rectangular solid) with subdivisions based on a .png file.  My goal is to print out the final product and then hand color or paint it using raised topology as a guide, so it is necessary to modify the mesh, not just apply a, say, bitmap.

I've tried several tutorials on the internet without success.  Ideally, I would like to use just Blender, but I have access to GIMP as well.  And I would like to avoid a single use tool, but eventually I'll give in and do it if I have to.

I've seen references to converting an image to Grease Pencil and then to Bezier Curves, but I couldn't get it to create a Grease Pencil object.

I tried using a texture to modify a subdivision surface, but nothing seemed to happen.

I'd be happy to use geometry nodes, as well.

But what I need is a very simple, efficient workflow to use a PNG or JPG with a smattering of dots into raised bumps on a flat mesh.

Here are 2 very simple images to illustrate what I'm trying to do.

 

Figure 2: Simple mesh

Figure 3: Simplified outcome, showing perpendicular extrusion

1. I drew a low resolution image using GIMP
2. I imported the PNG using Add > Image > Images as Planes [needs config]
3. I subdivided by 100 using Edit Mode >  A > Edge > Subdivide > Number of Cuts: 10 , Repeat

Figure 4: Subdividing the Plane ( at 10 x 10)

1. I added a Displace: Modifiers > Deform > Displace
2. Built a texture with the image: Texture > Open 
3. Set the displace texture
4. Set displace strength to -0.2

And it mocks me.

Figure 5: Clearly, I need another approach

Next up, Geometry Nodes!