340 Duster oil looks milky

Your side view of the oil in the container looks exactly like that from an engine that I am rebuilding now.. the grey layer at the bottom is an emulsion of oil and a small amount of water. My engine had a 1/2" hairline crack in the one of the combustion chambers so that was the reason. So I suspect very much you have a coolant leak; you at least have to assume that until proven otherwise. Head gasket, bad part, warped head or block, cracks... who knows. A very slow coolant leak will show up like your oil in the pix after sitting a few days, and not get milky.

To be sure, do as said above with a pressure test on a full cooling system. 2 tests: Cold and not running, apply 12-15 pis presure to the full cooling system, shut off the air soursce and watch for the pressure to drop. I'd do it warm and running....you get a running pressure gauge that clamps onto the rad cap spout on the rad, run the engine and warm it up, and watch for pressure pulses or fluctuations on the gauge. Sometimes you can borrow those gauges from the parts stores...

And honestly, for running 5 minutes, in a so called rebuilt engine, the oil looks filthy. I'll guess that the prior owners did not do crap the clean up the block, etc., and the gas that you got in the engine from the bad carb washed it down and it is now in the pan and oil system. Keep in mind that any small crud in the pan goes right into the oil pump and chews on it, as the pump is before the filter.