Use a 1/8" spiral and, hard board for the tenon.
You didn't specify the length of the piece that gets the end mortise. You'll ned a carrier board to hold the piece and ride the fence, with a 90 degree stop. I'd use toggle clamps attached to the stop.
The other alternative is to rout or saw a tenon on the end and forget the loose tenon.
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Last edited by Gene Howe; 11-12-2017 at 11:18 AM.