The different pieces of wood I picked up varied from 0.124in - 0.140in depending on the piece. I preferred the look and feel of the lid slightly below flush, so what I did was use my SO3 to cut out the lid and make the 0.25in dia x 0.0625in deep holes for the magnets (0.25in dia x 0.063in thick from KJMagnetics).
Then I epoxied the magnets in and measured the thickness. Since I just clamped the wood strips down and they flexed a bit, sometimes the hole was not exactly the depth I wanted, so I would epoxy them in before measuring the final thickness of the lid.
I made the cut out for the lid to be the total thickness with magnets + 0.03in so the lid was just slightly below flush. Then I would make the magnet holes in the board (using 0.25in dia x 0.25in thick magnets) deep enough so I could put them just below flush. Then the magnets would hold, but not cause the lid to protrude above flush.