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The most expensive tool is the one you buy "cheaply" and often...
A good dowel jig (Jessem) also will reference off the same face. The lateral registration (getting the stripes aligned) will depend somewhat on you being careful. I don't own a Domino, but isn't that the case with it as well?
Make it with the weak joint then flip it over. Rout out half the thickness over most of the area, staying clear of the edges. Fill with a solid piece.
How about a giant half lap joint, if that is the correct term for it. The colors would be reversed on the back side.