Having gone through the same trials and tribulations myself, and learning from @jbmanning5, here is what to do next time. Take the masking off first. The amount of toasting of the image with an engrave, in my experience isn’t that bad, especially with how little white you have. Ignore the puzzle cuts for now, and engrave the image on whatever will be the front.
When the engrave is done, and without doing anything in the GFUI, mark your corners with tape on the crumb tray (or some other means to register it) and flip the wood over, leaving the masking on, ignore the image, and cut the puzzle pieces. This does two things - keeps the smoke burn on the back, and the resulting cut lines are much narrower on the bottom. The bottom is now your front.
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