I have seen a boxlock that had the cheeks built up with matching wood.
After staining as needed, it was almost impossible to see.... until you knew.
Seems like a workable method.

=Any experience with using veneer? I have walnut +0.064 mm thickness that would raise the level to match the metal and allow for sanding to flush. I have not tried veneer before but might try it. Would be blended in and finished to match the stock color.