I plowed a groove in a piece of wood that was the depth I wanted the piece to be and chiseled a square stop in the end. Probably makes more sense with pictures (goes out to shop and re-creates the experience).
This took about 10 minutes - I plowed a groove in a piece of oak with a plow and router plane to just a bit shallower than I wanted the strip to be (the plow can't go right up to the stop so I used the router plane to finish that - I could use a powered router or whatever to cut the groove - you could even do a through cut with a dado blade and put in an insert for a stop or.. well dozens of ways to cut a stopped groove I guess ).
In this case its about 3/16" or so deep but I've done down to 1/16" pieces like this with success (it gets a bit harder the thinner they are alright, down to about 1/8" isn't to bad).
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Put the piece in the groove (in this case I didn't even need the stopped end, since it was tight enough to be tapped in, but after a few dozen strips .. I'd need the stop)
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4-5 passes with the smoothing plane and its shiny smooth (which you probably can't tell the difference because my camera takes potato quality pictures if the light is a bit low).
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If you need to stop the plane at a specific depth put some low friction tape on the sides of it fore and aft of the blade to build up a stop and wax the heck out of the block (or double stick tape thin strips of hardwood or brass to the bottom). You have to replace the tape every so often if you do that. I just practiced getting better at where I wanted to stop.. not perfect, but decidedly well into mediocre after a while.
I did a bit over 100 pieces like this that were all pretty consistent (less than 1/64" difference) on 4 sides and then once I was done bought a drum sander for the next batch - which I never did
. The drum sander has been handy for plenty of other projects though so no regrets.