I call bullshit on "Ceramic rods leave a fairly toothy edge."
Some do, some don't. DMT CS2s, Idahones, and MAC Blacks don't. Those three are roughly equivalent to 2K JIS.
Most people don't know how to use a rod without weakening the edge and making it more chip prone; most probably actually chip the rod as part of their steeling practice. Few strokes, very light pressure, never bang the knife against the rod. Bad steeling technique could be part of your problem. If you have the time and the interest, read Steeling Away
Chipping is endemic to poly boards. The knife bites into the board. The board holds the knife, and if the user torques the knife while it's in the board, the edge tends to chip. The problem is substantially worse with a toothy blade or a wire edge.
If you tend to chip right after you sharpen, it's very likely you're not deburring all the way after sharpening.