Dan,

You asked

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Does anyone have any experience with a wood tap and die set like this one:

https://taytools.com/products/wood-tap-die-sets?variant=18507395498035
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I have used similar tools with some success. The one word in the description I
would quibble with is "effortlessly". In my experience, they are a bit finickity
to adjust and use. The cutter needs to be sharp and adjusted just so. I suggest
setting the cutter for a light cut at first, increasing the depth of cut
incrementally on subsequent passes. On subsequent passes be careful to center
the cutter in the groove. Also, be careful when sharpening not to mess up the
cutter's geometry.

If you are using store-bought dowels, be sure to check that the dowel is in fact
round and that it is the size the seller says it is.

Don't ask me how I learned these things. :-)

Good luck!

Chuck Taylor
north of Seattle USA