it sounds like the crack is an indication that the glue joint is opening up and will most likely continue unless you provide a new strong glue joint. Any filler or epoxy is covering up a problem and can't provide a really complete fix.

I would use at least a 1/4" bit and make it a good 1/2" deep. Also extend the cut about two inches beyond the end of the visible crack to make sure the Dutchman includes any separation not visible on the surface.

If you take your time in selecting a piece of teak for color and straight grain the Dutchman should blend in well with the existing wood. It's a lot more work than just smearing something in the crack but it is permanent. IMHO.