if it were me I’d fool with curves in gimp/ps. (I mostly use GIMP, so adjust as needed)
** highly theoretical workflow incoming **
Crop out a very small test area of your gradient-ed image. You are going to be iterating, so you want to make this only as large as you need to get a good test to save time and materials.
Engrave your test piece. Look at the actual curved surface you got.
This is where it gets weird and may not work:
Go into your color curves (This is a greyscale image, yeah?)
Draw your curve to be roughly the “reverse” of the curve you observed in your first engrave. That is, if your material curve is slightly convex, make your color curve slightly concave, or vice versa. Make some sort of note or screenshot or something to see exactly what curve you’re using.
Engrave again. Check results.
If it isn’t right: UNDO a few times to get your gradient back to the start. This will be important in a sec. Redraw your curve knowing what you know now and try again. Repeat until satisfied.
I’d suspect after a couple tries you can get the gradient curve pretty dialed in.
Now that you know what the final curve should be (You were taking screenshots, right? RIGHT?), go apply that to your original image. This is why we kept UNDOing between runs, you need to know what a single operation “fixer” curve looks like.
Of course, there is probably a more precise way to save and reproduce a curve, I have just never tried to do so.