The chippers in a dado set aren't made for outside cuts. They can
burn and kick back. Actually, I'm surprised that a blade plus the one
chipper gave you a 3/16" cut - the cutting edge on the chipper is
wider than 1/16", and your dado should have been too wide even before
the cardboard spacer.
Others have mentioned moving the fence, a wobble dado and router bits
- all of which will work.
Another option is a set of wobble washers. These are sets of four
tapered washers - tow on each side of your saw blade. You can adjust
the wobble from none at all up to a 3/4" or so dado. I wouldn't use
them for a wide dado, as you get a rounded bottom, but for 3/16" you
wouldn't notice. I'm not sure who sells them today, but think Sears
carried them at least in the past. They're cheap, by the way.
You could always widen the 1/8" kerf from your regular saw blade with
a side rabbet plane. I wouldn't use a single dado saw blade - they
are ground to cut cleanly on one side only.
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