I have an idea how to make your image painted on wood veneer surface a durable way. Preliminarily need to prepare a solution from 10 parts of blue vitriol, 6 parts of lampblack and 3 parts of pure alcohol. Then make an outline with blue color pencil on the front-face area. After that cover an outlined space with crow-quill, but before dip it in prepared solution. Such solution penetrates into the wood very deep.
Wait until your image will dry out and then place veneer under permanent and weak water flow. It must be uninterruptedly washing out for 20 hours.
Using such processing image penetrates so deep into the veneer that contour clearly could be viewed on opposite side. Thus, image won't become corrupted anyway.