Nat, while I don't have experience with your model Perkins, we did have a similar problem with the Yanmar on the Islander. It ran smooth the entire time we owned the boat, when the new owner and broker took possession and tried to move it to another marina they had a situation develop as you described. The oil overflowed but their was no evidence of coolant or water, just a mysterious condition of making its own oil. I would not let the new owner take it as-is so contracted with a local diesel mechanic to fix it. Besides the extra oil, it was also down on power and a little hard to start. While the mechanic tried several things including rebuilding the injectors, it ended up being a failing diaphragm and seal in the mechanical fuel pump mounted on the engine. It had not failed completely, only enough to allow diesel to get through the seal when under pressure, that was a straight shot into the internal oil reservoir. It was also the reason the engine was low on power, just enough fuel getting to the injector pump to start and run, not enough to make full power. I'm not sure about your reference to a "lift pump", we had a lift pump on the IP which was an electric pump in line before the mechanical Yanmar pump.
Good luck. Craig