Why not place a long strip of the 1/4" top of the knob material and drill the holes for the knob through both pieces of material? The hole saw will cut the knob and the top at the same time. (some double sided tape is required to keep both pieces together during drilling). Adjust the depth of the pilot bit in the large hole saw so that it does not pierce the top.
One saw cut for the long strip and no need to use the drop saw for squares or to sand the indents in the top piece.
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