My guess is the ground cable from the battery to the engine block isn't making good contact at the block. Oil will leak down into the connection and get loaded up with dirt. First disconnect the battery. Then I would disconnect that lower ground connection and clean it then screw it back together good and tight. After that I'd do the same with the wire that goes down from the starter solenoid to the starter and be sure it is also super clean. You said you put in a new starter. Did you do a good job of cleaning the bolts and bell housing face to make sure a good ground was going through it also?