Kohler CV23S Running Very Rich

I've got a Kohler CV23S-75520 (S/N 3111936801) on a 2001(?) Dixon ZTR5023 (has about 650 hours) that is running extremely rich at all throttle speeds. Lower than half throttle it is visibly puffing tons of black smoke out, and plugs are very black with carbon.

So far I've changed out the fuel filter, all fuel lines from both tanks up to the carburetor, and also cleaned the carburetor. I read somewhere that the issue could be caused by a worn out accelerator pump on the carburetor. This...

Kohler CV23S Running Very Rich