That, exactly. And IMO the result after going DF -> DE -> SJ is underwhelming. The diamonds leave a rather sparse scratch pattern that's hard to get rid of entirely.
So if you really want to start with the DF, i would recommend DF->SG ungraded -> SG graded fine -> SJ.
So if you really want to start with the DF, i would recommend DF->SG ungraded -> SG graded fine -> SJ.