I f you absolutely must have the flat bottom then use a thinner piece
and cut a through mortise. When that is done, glue a thin piece across
the bottom to close off the square holes.


That is a good idea.

Getter yet, rip a grove with a dado blade down to the finished deptth of the
mortises and fill the groove with additional stock.

Depending on the design this may be a bit more hidden.

-Steve



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