Before you drop the pan get a combustion gas detection kit. That should rule out or confirm head gasket. You can pressure it up and see if you can make the water pump leak externally, sometimes the weep hole gets plugged forcing an internal leak although why it would just start leaking sitting I can't say.For random unexplained water in oil I'd say the liners themselves might be ate up if the ph of the coolant hasn't been kept in check or a previous owner used cheap parts to O/H it. I've seen cheap liners in a Cat C15 barely make it a year.
It's a Dash 3 so it's OLD. Might be age or hours but you in the range for problems anyway you look at it.That engine might have copper sleeves for the injectors. Pull the valve cover and look for coolant sitting in low areas of the head. Soft plugs or dimples and such. All the other leaks previously mentioned are still in play.Good luck!
If I were you I'd pull the valve covers and clean them, change the oil and filters, run it a couple hours hard and change em again. Then run hard and see if you still have cross contamination. Milkshake ain't gonna get in the valve covers unless she's been run while leaking or had a bunch of start up and shut downs before getting up to temp.Pulling the drain plug will tell you if you need to go any further. If you pull it and see steady coolant, you need to go deeper, if its black oil followed by sludge, probably just need to change oil and work her hard
If you have a high level of coolant first, your buds are absolutely right. Best , quickest path to discovery is drop the pan and pump her up