"Running In" oils quite often are less sophisticated than "normal" oils. The idea is that parts, such as piston rings and bores can bed to (Wear ) to each other. It used to be that many years ago, colloidal graphite was added to the oil, this may have been good for the bearings, but did little to improve ring bedding.
I have come across a special "running in" fuel for diesel engines. It contained a very slight abrasive which was delivered into the cylinder to improve ring bedding.
Modern cylinder liner honing techniques such as plateau honing have done much to reduce running in times. Although the modern car probably takes a bout 20K miles before it really beds in properly.
Having had an engine returned for oil passing in to the exhaust, (Caused by bore glazing from running for long periods at high idle to set reel speed on a combine harvester, ) The solution was to run it at full load rated speed for hours on end. Eventually, the rings wore through the glaze and oil control began to improve.
Probably the best thing is to run the engine under gradually increasing loads and speeds, finishing up with a run at full speed, full load. The load is probably more important than the sped.
When we were on holiday in USA one tear we hired a car to drive from Atlanta to Florida and onto Oklahoma and return. Probably the car had never travelled more than 20 miles at a time.
On the morning of day 2, the car had consumed a lot of oil, but as each day passed the oil consumed reduced, until by the time that we handed it back it was no longer using oil. We had spent a fortnight running it in!
Howard