Some well-disguised ribbon knots

For certain knots J in S1 × D2, the dual knot J∗ in S1 × D2 is defined. Let J(O) be the satellite knot of the unknot O with pattern J, and K be the satellite of J(O) with pattern J∗. The knot K then bounds a smooth disk in a 4-ball, but is not obviously a ribbon knot. We show that K is, in fact, ribbon. We also show that the connected sum J(O) # J∗(O) is a nonribbon knot for which all known algebraic obstructions to sliceness vanish.