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That's not really possible with the type of laser that is commonly found and used for engraving. If you change the focus from the front of the panel to the middle, it will still effect the front, but the engraving will be unfocused and possibly uneven. Turning the power up or the speed down on the laser will produce a deeper engraving, and flipping the illustration and engraving from the rear will leave the front surface smooth and may look better in this application.Source: I do this 80 hours per week
Using a damp cloth while sanding is actually a technique called raising the grain. It will cause the ends of the woodgrain to stand up a bit. If you sand it while they're raised, they won't raise again if it gets wet, and it can help you to get a smoother finish.