after engine break in

at after the 200klm time how do you then change the oil to synthetic based oil and know which viscosity oil and weight that needs to be used according to your build. As with my engine, this manufacturers spec oil standard is 0 - w50 so after using different pistons and new ring gaps and so on for supercharging which oil now would be the appropriate oil weight

The pistons and rings don't really have much impact on the oil we'd choose to run. It's more to do with your bearings and specifically the bearing clearances, and the way the engine will be used. Generally if I'm adding forced induction to a stock engine I may decide to move to a thicker oil in order to provide a thicker and stronger oil film. This needs to be done in conjunction with monitoring the oil pressure in use. A good example would be our Subaru FA20. In stock form this is specified to run a 0W-20 oil. The engine is still stock although we are now making around double the stock power thanks to a turbo and E85 fuel. I now use a 10W-40 oil to offer more protection and higher oil pressure on track.

In your example I don't really have enough information to advise but I'd be suggesting you consider perhaps a 10W-50 or 15W-50.

Those light weight oil specs you see on new cars are mostly to get a tiny fuel economy benefit.