340 Duster oil looks milky

Mechanical fuel pump? Maybe a pinhole tear in the diaphragm.
Yep, or a dibbling leak in the carb allowing raw gas in the intake after engine shut off, and gas runs into the cylinders and past the rings. Too high a float might do it....

Happened to my /6 after some years of exactly that with the PO; he just was not aware. The first oil came out reeeeealy thin when I bought it, and the cylinders had to be bored .040" over to correct for all the severe bore wear from the repeated cylinder washings, especially #1.